Theorem iffalsei 3614

Description: Inference associated with iffalse 3613. (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 3613	. 2 |- ( -. ph -> if ( ph , A , B ) = B )
3	1, 2	ax-mp 5	1 |- if ( ph , A , B ) = B

Syntax hints:   -. wn 3   = wceq 1397   ifcif 3605

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 716  ax-5 1495  ax-7 1496  ax-gen 1497  ax-ie1 1541  ax-ie2 1542  ax-8 1552  ax-11 1554  ax-4 1558  ax-17 1574  ax-i9 1578  ax-ial 1582  ax-i5r 1583  ax-ext 2213

This theorem depends on definitions:  df-bi 117  df-nf 1509  df-sb 1811  df-clab 2218  df-cleq 2224  df-clel 2227  df-if 3606

This theorem is referenced by:  0tonninf  10701  sum0  11948  prod0  12145  ennnfonelem1  13027  vtxval0  15903  iedgval0  15904  nnnninfex  16624  dcapnconst  16665