Theorem ex-natded5.2-2

Description: A more efficient proof of Theorem 5.2 of Clemente p. 15. Compare with ex-natded5.2 and ex-natded5.2i . (Contributed by Mario Carneiro, 9-Feb-2017) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	ex-natded5.2.1	|- ( ph -> ( ( ps /\ ch ) -> th ) )
	ex-natded5.2.2	|- ( ph -> ( ch -> ps ) )
	ex-natded5.2.3	|- ( ph -> ch )
Assertion	ex-natded5.2-2	|- ( ph -> th )

Proof

Step	Hyp	Ref	Expression
1		ex-natded5.2.1	|- ( ph -> ( ( ps /\ ch ) -> th ) )
2		ex-natded5.2.2	|- ( ph -> ( ch -> ps ) )
3		ex-natded5.2.3	|- ( ph -> ch )
4	3 2	mpd	|- ( ph -> ps )
5	4 3 1	mp2and	|- ( ph -> th )