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Theorem ex-natded5.2-2 20780
Description: A more efficient proof of Theorem 5.2 of [Laboreo] p. 15. Compare with ex-natded5.2 20779 and ex-natded5.2i 20781. (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 16 . 2  |-  ( ph  ->  ps )
4 ex-natded5.2.1 . 2  |-  ( ph  ->  ( ( ps  /\  ch )  ->  th )
)
53, 1, 4mp2and 663 1  |-  ( ph  ->  th )
Colors of variables: wff set class
Syntax hints:    -> wi 6    /\ wa 360
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10
This theorem depends on definitions:  df-bi 179  df-an 362
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