Theorem iffalsei 3510

Description: Inference associated with iffalse 3509. (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 3509	. 2 |- ( -. ph -> if ( ph , A , B ) = B )
3	1, 2	ax-mp 5	1 |- if ( ph , A , B ) = B

Syntax hints:   -. wn 3   = wceq 1332   ifcif 3501

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in2 605  ax-io 699  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1481  ax-11 1483  ax-4 1487  ax-17 1503  ax-i9 1507  ax-ial 1511  ax-i5r 1512  ax-ext 2136

This theorem depends on definitions:  df-bi 116  df-nf 1438  df-sb 1740  df-clab 2141  df-cleq 2147  df-clel 2150  df-if 3502

This theorem is referenced by:  0tonninf  10316  sum0  11262  prod0  11459  ennnfonelem1  12087  dcapnconst  13572