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  7497  elpq  9840  elfz0ubfz0  10317  elfzmlbp  10324  fzo1fzo0n0  10379  elfzo0z  10380  fzofzim  10384  elfzodifsumelfzo  10402  swrdswrd  11232  swrdccatin1  11252  p1modz1  12300  dfgcd2  12530  algcvga  12568  pcprendvds  12808  usgruspgrben  15978