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  7681  elpq  10049  elfz0ubfz0  10532  elfzmlbp  10539  fzo1fzo0n0  10595  elfzo0z  10596  fzofzim  10600  elfzodifsumelfzo  10619  swrdswrd  11477  swrdccatin1  11497  p1modz1  12561  dfgcd2  12791  algcvga  12829  pcprendvds  13069  usgruspgrben  16427  trlf1  16629