Theorem iffalsei 3402

Description: Inference associated with iffalse 3401. (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 3401	. 2 |- ( -. ph -> if ( ph , A , B ) = B )
3	1, 2	ax-mp 7	1 |- if ( ph , A , B ) = B

Syntax hints:   -. wn 3   = wceq 1289   ifcif 3393

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 580  ax-io 665  ax-5 1381  ax-7 1382  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-8 1440  ax-11 1442  ax-4 1445  ax-17 1464  ax-i9 1468  ax-ial 1472  ax-i5r 1473  ax-ext 2070

This theorem depends on definitions:  df-bi 115  df-nf 1395  df-sb 1693  df-clab 2075  df-cleq 2081  df-clel 2084  df-if 3394

This theorem is referenced by:  0tonninf  9845  sum0  10780