Theorem simplbi2 382

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 132	. 2 |- ( ( ps /\ ch ) -> ph )
3	2	ex 114	1 |- ( ps -> ( ch -> ph ) )

Syntax hints:   -> wi 4   /\ wa 103   <-> wb 104

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107

This theorem depends on definitions:  df-bi 116

This theorem is referenced by:  pm5.62dc  929  pm5.63dc  930  simplbi2com  1420  reuss2  3356  elni2  7122  elfz0ubfz0  9902  elfzmlbp  9909  fzo1fzo0n0  9960  elfzo0z  9961  fzofzim  9965  elfzodifsumelfzo  9978  dfgcd2  11702  algcvga  11732