Theorem simplbi2 377

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 131	. 2 |- ( ( ps /\ ch ) -> ph )
3	2	ex 113	1 |- ( ps -> ( ch -> ph ) )

Syntax hints:   -> wi 4   /\ wa 102   <-> wb 103

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106

This theorem depends on definitions:  df-bi 115

This theorem is referenced by:  pm5.62dc  886  pm5.63dc  887  simplbi2com  1373  reuss2  3244  elni2  6504  elfz0ubfz0  9136  elfzmlbp  9143  fzo1fzo0n0  9192  elfzo0z  9193  fzofzim  9197  elfzodifsumelfzo  9210  dfgcd2  10403  ialgcvga  10433