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Theorem ex-natded5.2i 25254
Description: The same as ex-natded5.2 25252 and ex-natded5.2-2 25253 but with no context. (Proof modification is discouraged.) (New usage is discouraged.) (Contributed by Mario Carneiro, 9-Feb-2017.)
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
StepHypRef Expression
1 ex-natded5.2i.3 . . . 4  |-  ch
2 ex-natded5.2i.2 . . . 4  |-  ( ch 
->  ps )
31, 2ax-mp 5 . . 3  |-  ps
43, 1pm3.2i 455 . 2  |-  ( ps 
/\  ch )
5 ex-natded5.2i.1 . 2  |-  ( ( ps  /\  ch )  ->  th )
64, 5ax-mp 5 1  |-  th
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    /\ wa 369
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 185  df-an 371
This theorem is referenced by: (None)
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