Theorem iffalsei 4096

Description: Inference associated with iffalse 4095. (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 4095	. 2 |- ( -. ph -> if ( ph , A , B ) = B )
3	1, 2	ax-mp 5	1 |- if ( ph , A , B ) = B

Syntax hints:   -. wn 3   = wceq 1483   ifcif 4086

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-9 1999  ax-10 2019  ax-11 2034  ax-12 2047  ax-13 2246  ax-ext 2602

This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-tru 1486  df-ex 1705  df-nf 1710  df-sb 1881  df-clab 2609  df-cleq 2615  df-clel 2618  df-if 4087

This theorem is referenced by:  sum0  14452  prod0  14673  prmo4  15835  prmo6  15837  itg0  23546  vieta1lem2  24066  vtxval0  25931  iedgval0  25932  ex-prmo  27316  dfrdg2  31701  dfrdg4  32058  fwddifnp1  32272  bj-pr21val  33001  bj-pr22val  33007  clsk1indlem4  38342  clsk1indlem1  38343  refsum2cnlem1  39196  limsup10ex  40005  iblempty  40181  fouriersw  40448