Theorem pm2.61ddan 767

Description: Elimination of two antecedents. (Contributed by NM, 9-Jul-2013.)

Hypotheses

Ref	Expression
pm2.61ddan.1	|- ((ph /\ ps) -> th)
pm2.61ddan.2	|- ((ph /\ ch) -> th)
pm2.61ddan.3	|- ((ph /\ (-. ps /\ -. ch)) -> th)

Assertion

Ref	Expression
pm2.61ddan	|- (ph -> th)

Proof of Theorem pm2.61ddan

Step	Hyp	Ref	Expression
1		pm2.61ddan.1	. 2 |- ((ph /\ ps) -> th)
2		pm2.61ddan.2	. . . 4 |- ((ph /\ ch) -> th)
3	2	adantlr 695	. . 3 |- (((ph /\ -. ps) /\ ch) -> th)
4		pm2.61ddan.3	. . . 4 |- ((ph /\ (-. ps /\ -. ch)) -> th)
5	4	anassrs 629	. . 3 |- (((ph /\ -. ps) /\ -. ch) -> th)
6	3, 5	pm2.61dan 766	. 2 |- ((ph /\ -. ps) -> th)
7	1, 6	pm2.61dan 766	1 |- (ph -> th)

Syntax hints:  -. wn 3   -> 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: (None)