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  958  pm5.63dc  959  simplbi2com  1494  reuss2  3513  elni2  7671  elpq  10028  elfz0ubfz0  10510  elfzmlbp  10517  fzo1fzo0n0  10573  elfzo0z  10574  fzofzim  10578  elfzodifsumelfzo  10597  swrdswrd  11455  swrdccatin1  11475  p1modz1  12539  dfgcd2  12769  algcvga  12807  pcprendvds  13047  usgruspgrben  16341  trlf1  16543