Theorem simplbi2 385

Description: Deduction eliminating a conjunct. (Contributed by Alan Sare, 31-Dec-2011.)

Hypothesis

Ref	Expression
pm3.26bi2.1	|- ( ph <-> ( ps /\ ch ) )

Assertion

Ref	Expression
simplbi2	|- ( ps -> ( ch -> ph ) )

Proof of Theorem simplbi2

Step	Hyp	Ref	Expression
1		pm3.26bi2.1	. . 3 |- ( ph <-> ( ps /\ ch ) )
2	1	biimpri 133	. 2 |- ( ( ps /\ ch ) -> ph )
3	2	ex 115	1 |- ( ps -> ( ch -> ph ) )

Syntax hints:   -> wi 4   /\ wa 104   <-> wb 105

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

This theorem depends on definitions:  df-bi 117

This theorem is referenced by:  pm5.62dc  951  pm5.63dc  952  simplbi2com  1487  reuss2  3485  elni2  7524  elpq  9873  elfz0ubfz0  10350  elfzmlbp  10357  fzo1fzo0n0  10412  elfzo0z  10413  fzofzim  10417  elfzodifsumelfzo  10436  swrdswrd  11276  swrdccatin1  11296  p1modz1  12345  dfgcd2  12575  algcvga  12613  pcprendvds  12853  usgruspgrben  16025  trlf1  16183