Theorem iffalsei 3588

Description: Inference associated with iffalse 3587. (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 3587	. 2 |- ( -. ph -> if ( ph , A , B ) = B )
3	1, 2	ax-mp 5	1 |- if ( ph , A , B ) = B

Syntax hints:   -. wn 3   = wceq 1373   ifcif 3579

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 616  ax-io 711  ax-5 1471  ax-7 1472  ax-gen 1473  ax-ie1 1517  ax-ie2 1518  ax-8 1528  ax-11 1530  ax-4 1534  ax-17 1550  ax-i9 1554  ax-ial 1558  ax-i5r 1559  ax-ext 2189

This theorem depends on definitions:  df-bi 117  df-nf 1485  df-sb 1787  df-clab 2194  df-cleq 2200  df-clel 2203  df-if 3580

This theorem is referenced by:  0tonninf  10622  sum0  11814  prod0  12011  ennnfonelem1  12893  vtxval0  15765  iedgval0  15766  nnnninfex  16161  dcapnconst  16202