Theorem iftruei 3357

Description: Inference associated with iftrue 3356. (Contributed by BJ, 7-Oct-2018.)

Hypothesis

Ref	Expression
iftruei.1	|- ph

Assertion

Ref	Expression
iftruei	|- if ( ph , A , B ) = A

Proof of Theorem iftruei

Step	Hyp	Ref	Expression
1		iftruei.1	. 2 |- ph
2		iftrue 3356	. 2 |- ( ph -> if ( ph , A , B ) = A )
3	1, 2	ax-mp 7	1 |- if ( ph , A , B ) = A

Syntax hints:   = wceq 1284   ifcif 3351

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-in2 577  ax-io 662  ax-5 1376  ax-7 1377  ax-gen 1378  ax-ie1 1422  ax-ie2 1423  ax-8 1435  ax-11 1437  ax-4 1440  ax-17 1459  ax-i9 1463  ax-ial 1467  ax-i5r 1468  ax-ext 2063

This theorem depends on definitions:  df-bi 115  df-nf 1390  df-sb 1686  df-clab 2068  df-cleq 2074  df-clel 2077  df-if 3352

This theorem is referenced by:  xnegpnf  8895  xnegmnf  8896  exp0  9480  lcm0val  10447