Theorem pm5.74da 668

Description: Distribution of implication over biconditional (deduction rule). (Contributed by NM, 4-May-2007.)

Hypothesis

Ref	Expression
pm5.74da.1	|- ((ph /\ ps) -> (ch <-> th))

Assertion

Ref	Expression
pm5.74da	|- (ph -> ((ps -> ch) <-> (ps -> th)))

Proof of Theorem pm5.74da

Step	Hyp	Ref	Expression
1		pm5.74da.1	. . 3 |- ((ph /\ ps) -> (ch <-> th))
2	1	ex 423	. 2 |- (ph -> (ps -> (ch <-> th)))
3	2	pm5.74d 238	1 |- (ph -> ((ps -> ch) <-> (ps -> th)))

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:  ralbida  2629