Theorem anc2l 538

Description: Conjoin antecedent to left of consequent in nested implication. (Contributed by NM, 10-Aug-1994.) (Proof shortened by Wolf Lammen, 14-Jul-2013.)

Assertion

Ref	Expression
anc2l	|- ((ph -> (ps -> ch)) -> (ph -> (ps -> (ph /\ ch))))

Proof of Theorem anc2l

Step	Hyp	Ref	Expression
1		pm5.42 531	. 2 |- ((ph -> (ps -> ch)) <-> (ph -> (ps -> (ph /\ ch))))
2	1	biimpi 186	1 |- ((ph -> (ps -> ch)) -> (ph -> (ps -> (ph /\ ch))))

This proof depends on syntax axioms:   -> wi 4   /\ 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: (None)