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Theorem ex-natded5.2-2 20792
Description: A more efficient proof of Theorem 5.2 of [Clemente] p. 15. Compare with ex-natded5.2 20791 and ex-natded5.2i 20793. (Contributed by Mario Carneiro, 9-Feb-2017.)
Hypotheses
Ref Expression
ex-natded5.2.1  |-  ( ph  ->  ( ( ps  /\  ch )  ->  th )
)
ex-natded5.2.2  |-  ( ph  ->  ( ch  ->  ps ) )
ex-natded5.2.3  |-  ( ph  ->  ch )
Assertion
Ref Expression
ex-natded5.2-2  |-  ( ph  ->  th )

Proof of Theorem ex-natded5.2-2
StepHypRef Expression
1 ex-natded5.2.3 . . 3  |-  ( ph  ->  ch )
2 ex-natded5.2.2 . . 3  |-  ( ph  ->  ( ch  ->  ps ) )
31, 2mpd 14 . 2  |-  ( ph  ->  ps )
4 ex-natded5.2.1 . 2  |-  ( ph  ->  ( ( ps  /\  ch )  ->  th )
)
53, 1, 4mp2and 660 1  |-  ( ph  ->  th )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 358
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
This theorem depends on definitions:  df-bi 177  df-an 360
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