Theorem pm5.3 692

Description: Theorem *5.3 of [WhiteheadRussell] p. 125. (Contributed by NM, 3-Jan-2005.) (Proof shortened by Andrew Salmon, 7-May-2011.)

Assertion

Ref	Expression
pm5.3	|- (((ph /\ ps) -> ch) <-> ((ph /\ ps) -> (ph /\ ch)))

Proof of Theorem pm5.3

Step	Hyp	Ref	Expression
1		impexp 433	. 2 |- (((ph /\ ps) -> ch) <-> (ph -> (ps -> ch)))
2		imdistan 670	. 2 |- ((ph -> (ps -> ch)) <-> ((ph /\ ps) -> (ph /\ ch)))
3	1, 2	bitri 240	1 |- (((ph /\ ps) -> ch) <-> ((ph /\ ps) -> (ph /\ ch)))

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: (None)