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  954  pm5.63dc  955  simplbi2com  1490  reuss2  3489  elni2  7577  elpq  9927  elfz0ubfz0  10405  elfzmlbp  10412  fzo1fzo0n0  10468  elfzo0z  10469  fzofzim  10473  elfzodifsumelfzo  10492  swrdswrd  11335  swrdccatin1  11355  p1modz1  12418  dfgcd2  12648  algcvga  12686  pcprendvds  12926  usgruspgrben  16110  trlf1  16312