Theorem pm2.61dda 834

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

Hypotheses

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

Assertion

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

Proof of Theorem pm2.61dda

Step	Hyp	Ref	Expression
1		pm2.61dda.3	. . . 4 |- ( ( ph /\ ( ps /\ ch ) ) -> th )
2	1	anassrs 680	. . 3 |- ( ( ( ph /\ ps ) /\ ch ) -> th )
3		pm2.61dda.2	. . . 4 |- ( ( ph /\ -. ch ) -> th )
4	3	adantlr 751	. . 3 |- ( ( ( ph /\ ps ) /\ -. ch ) -> th )
5	2, 4	pm2.61dan 832	. 2 |- ( ( ph /\ ps ) -> th )
6		pm2.61dda.1	. 2 |- ( ( ph /\ -. ps ) -> th )
7	5, 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:  lhpexle1lem  35293  lclkrlem2x  36819