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Metamath Proof Explorer

Theorem ex-natded5.13-2

Description: A more efficient proof of Theorem 5.13 of Clemente p. 20. Compare with ex-natded5.13 . (Contributed by Mario Carneiro, 9-Feb-2017) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	ex-natded5.13.1	\|- ( ph -> ( ps \/ ch ) )
	ex-natded5.13.2	\|- ( ph -> ( ps -> th ) )
	ex-natded5.13.3	\|- ( ph -> ( -. ta -> -. ch ) )
Assertion	ex-natded5.13-2	\|- ( ph -> ( th \/ ta ) )

Proof

Step	Hyp	Ref	Expression
1		ex-natded5.13.1	\|- ( ph -> ( ps \/ ch ) )
2		ex-natded5.13.2	\|- ( ph -> ( ps -> th ) )
3		ex-natded5.13.3	\|- ( ph -> ( -. ta -> -. ch ) )
4	3	con4d	\|- ( ph -> ( ch -> ta ) )
5	2 4	orim12d	\|- ( ph -> ( ( ps \/ ch ) -> ( th \/ ta ) ) )
6	1 5	mpd	\|- ( ph -> ( th \/ ta ) )