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 ) )

This proof depends on syntax axioms:   -> wi 4   /\ wa 104   <-> wb 105

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

This proof depends on definitions:  df-bi 117

This theorem is used by:  pm5.62dc  958  pm5.63dc  959  simplbi2com  1494  reuss2  3513  elni2  7687  elpq  10066  elfz0ubfz0  10549  elfzmlbp  10556  fzo1fzo0n0  10612  elfzo0z  10613  fzofzim  10617  elfzodifsumelfzo  10636  swrdswrd  11499  swrdccatin1  11519  p1modz1  12586  dfgcd2  12816  algcvga  12854  pcprendvds  13098  usgruspgrben  16632  trlf1  16834