Theorem pm2.61dda

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

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

Proof

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