Theorem pm2.61ddan 833

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 751	. . 3 |- ( ( ( ph /\ -. ps ) /\ ch ) -> th )
4		pm2.61ddan.3	. . . 4 |- ( ( ph /\ ( -. ps /\ -. ch ) ) -> th )
5	4	anassrs 680	. . 3 |- ( ( ( ph /\ -. ps ) /\ -. ch ) -> th )
6	3, 5	pm2.61dan 832	. 2 |- ( ( ph /\ -. ps ) -> th )
7	1, 6	pm2.61dan 832	1 |- ( ph -> th )

Syntax hints:   -. wn 3   -> wi 4   /\ wa 384

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 197  df-an 386

This theorem is referenced by:  lgsdir2  25055  cdlemg24  35976