Theorem ex-natded5.2i 27263

Description: The same as ex-natded5.2 27261 and ex-natded5.2-2 27262 but with no context. (Contributed by Mario Carneiro, 9-Feb-2017.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
ex-natded5.2i.1	|- ( ( ps /\ ch ) -> th )
ex-natded5.2i.2	|- ( ch -> ps )
ex-natded5.2i.3	|- ch

Assertion

Ref	Expression
ex-natded5.2i	|- th

Proof of Theorem ex-natded5.2i

Step	Hyp	Ref	Expression
1		ex-natded5.2i.3	. . . 4 |- ch
2		ex-natded5.2i.2	. . . 4 |- ( ch -> ps )
3	1, 2	ax-mp 5	. . 3 |- ps
4	3, 1	pm3.2i 471	. 2 |- ( ps /\ ch )
5		ex-natded5.2i.1	. 2 |- ( ( ps /\ ch ) -> th )
6	4, 5	ax-mp 5	1 |- th

Syntax hints:   -> 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: (None)