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  10065  elfz0ubfz0  10548  elfzmlbp  10555  fzo1fzo0n0  10611  elfzo0z  10612  fzofzim  10616  elfzodifsumelfzo  10635  swrdswrd  11498  swrdccatin1  11518  p1modz1  12585  dfgcd2  12815  algcvga  12853  pcprendvds  13097  usgruspgrben  16649  trlf1  16851