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  3484  elni2  7512  elpq  9856  elfz0ubfz0  10333  elfzmlbp  10340  fzo1fzo0n0  10395  elfzo0z  10396  fzofzim  10400  elfzodifsumelfzo  10419  swrdswrd  11252  swrdccatin1  11272  p1modz1  12320  dfgcd2  12550  algcvga  12588  pcprendvds  12828  usgruspgrben  15999  trlf1  16126