Theorem imdistand 673

Description: Distribution of implication with conjunction (deduction rule). (Contributed by NM, 27-Aug-2004.)

Hypothesis

Ref	Expression
imdistand.1	|- (ph -> (ps -> (ch -> th)))

Assertion

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

Proof of Theorem imdistand

Step	Hyp	Ref	Expression
1		imdistand.1	. 2 |- (ph -> (ps -> (ch -> th)))
2		imdistan 670	. 2 |- ((ps -> (ch -> th)) <-> ((ps /\ ch) -> (ps /\ th)))
3	1, 2	sylib 188	1 |- (ph -> ((ps /\ ch) -> (ps /\ th)))

Syntax hints:   -> wi 4   /\ wa 358

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

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

This theorem is referenced by:  imdistanda  674  fconstfv  5457  nchoicelem19  6308