Theorem pm2.61dan 766

Description: Elimination of an antecedent. (Contributed by NM, 1-Jan-2005.)

Hypotheses

Ref	Expression
pm2.61dan.1	|- ((ph /\ ps) -> ch)
pm2.61dan.2	|- ((ph /\ -. ps) -> ch)

Assertion

Ref	Expression
pm2.61dan	|- (ph -> ch)

Proof of Theorem pm2.61dan

Step	Hyp	Ref	Expression
1		pm2.61dan.1	. . 3 |- ((ph /\ ps) -> ch)
2	1	ex 423	. 2 |- (ph -> (ps -> ch))
3		pm2.61dan.2	. . 3 |- ((ph /\ -. ps) -> ch)
4	3	ex 423	. 2 |- (ph -> (-. ps -> ch))
5	2, 4	pm2.61d 150	1 |- (ph -> ch)

This proof depends on syntax axioms:  -. wn 3   -> 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:  pm2.61ddan  767  pm2.61dda  768  ifeq1da  3688  ifeq2da  3689  ifclda  3690  ifbothda  3693  xpcan  5058  fvmpti  5700  fvmptss  5706