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  953  pm5.63dc  954  simplbi2com  1489  reuss2  3487  elni2  7533  elpq  9882  elfz0ubfz0  10359  elfzmlbp  10366  fzo1fzo0n0  10421  elfzo0z  10422  fzofzim  10426  elfzodifsumelfzo  10445  swrdswrd  11285  swrdccatin1  11305  p1modz1  12354  dfgcd2  12584  algcvga  12622  pcprendvds  12862  usgruspgrben  16036  trlf1  16238