Theorem simplbi2com 1333

Description: A deduction eliminating a conjunct, similar to simplbi2 367. (Contributed by Alan Sare, 22-Jul-2012.) (Proof shortened by Wolf Lammen, 10-Nov-2012.)

Hypothesis

Ref	Expression
simplbi2com.1	|- ( ph <-> ( ps /\ ch ) )

Assertion

Ref	Expression
simplbi2com	|- ( ch -> ( ps -> ph ) )

Proof of Theorem simplbi2com

Step	Hyp	Ref	Expression
1		simplbi2com.1	. . 3 |- ( ph <-> ( ps /\ ch ) )
2	1	simplbi2 367	. 2 |- ( ps -> ( ch -> ph ) )
3	2	com12 27	1 |- ( ch -> ( ps -> ph ) )

Syntax hints:   -> wi 4   /\ wa 97   <-> wb 98

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101

This theorem depends on definitions:  df-bi 110

This theorem is referenced by:  mo2r  1952  mo3h  1953  elres  4646  xpidtr  4715  peano5nnnn  6966  peano5nni  7917