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  10059  elfz0ubfz0  10542  elfzmlbp  10549  fzo1fzo0n0  10605  elfzo0z  10606  fzofzim  10610  elfzodifsumelfzo  10629  swrdswrd  11491  swrdccatin1  11511  p1modz1  12577  dfgcd2  12807  algcvga  12845  pcprendvds  13089  usgruspgrben  16525  trlf1  16727