Omission of 'if' in conditional.

[wotcha]

1.If I knew her phone number, I would call her.

2.Did I know her phone number, I would call her.

One of my grammar books say 2 is grammatically. Is it?

[5jj]

1.If I knew her phone number, I would call her.

2.Did I know her phone number, I would call her.

One of my grammar books say 2 is grammatically correct. Is it?

Not in most dialects of modern English.

[Raymott]

1.If I knew her phone number, I would call her.

2.Did I know her phone number, I would call her.

One of my grammar books say 2 is grammatically. Is it?

Sometimes 'if' is not necessary. For example:
"Had I known her phone number, I would have called her." This is the legitimate past tense equivalent of your sentence, which does not work in the present tense.

[Rover_KE]

I read a lot of American crime novels, and I've become aware in recent years of characters speaking colloquially omitting if in conditional sentences.

'You wanna keep your kneecaps intact, asshole, stay outta my face.'

Rover

[5jj]

I read a lot of American crime novels

Is that really something you want to be generally known?

[Raymott]

Is that really something you want to be generally known?

[Rover_KE]

Is that really something you want to be generally known?

I'll get my coat.

[5jj]

I'll get my coat.

How many times do I have to remind you about your hat?

[sparklingdark]

I just taught 1st, 2nd, and 3rd conditionals in an intermediate class, and the rule in the book was IF can only be omitted in the third conditional, like Raymott said.

You can instead use, Had I known and Otherwise.

[5jj]

I just taught 1st, 2nd, and 3rd conditionals in an intermediate class, and the rule in the book was IF can only be omitted in the third conditional, like Raymott said.

You can instead use, Had I known and Otherwise.

We can express conditions in several ways without if; it's just that wotcha's example is not possible in standard English.

If he comes/came - should he come
If he came - were he to come

If there is no pain, there can be no gain - No pain, no gain

If you don't stop, I'll shoot - Stop, or I'll shoot.
.....................................T Try to escape, and I'll shoot.