Theorem simplbi2com 1374

Description: A deduction eliminating a conjunct, similar to simplbi2 608. (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 608	. 2 |- (ps -> (ch -> ph))
3	2	com12 27	1 |- (ch -> (ps -> ph))

This proof depends on syntax axioms:   -> wi 4   <-> wb 176   /\ wa 358

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 177  df-an 360

This theorem is used by:  mo2  2233  2elresin  5195