Theorem iffalsei 3618

Description: Inference associated with iffalse 3617. (Contributed by BJ, 7-Oct-2018.)

Hypothesis

Ref	Expression
iffalsei.1	|- -. ph

Assertion

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

Proof of Theorem iffalsei

Step	Hyp	Ref	Expression
1		iffalsei.1	. 2 |- -. ph
2		iffalse 3617	. 2 |- ( -. ph -> if ( ph , A , B ) = B )
3	1, 2	ax-mp 5	1 |- if ( ph , A , B ) = B

Syntax hints:   -. wn 3   = wceq 1398   ifcif 3607

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-in2 620  ax-io 717  ax-5 1496  ax-7 1497  ax-gen 1498  ax-ie1 1542  ax-ie2 1543  ax-8 1553  ax-11 1555  ax-4 1559  ax-17 1575  ax-i9 1579  ax-ial 1583  ax-i5r 1584  ax-ext 2213

This theorem depends on definitions:  df-bi 117  df-nf 1510  df-sb 1811  df-clab 2218  df-cleq 2224  df-clel 2227  df-if 3608

This theorem is referenced by:  0tonninf  10765  sum0  12029  prod0  12226  ennnfonelem1  13108  vtxval0  15994  iedgval0  15995  nnnninfex  16748  dcapnconst  16794