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Theorem ex-natded5.3-2 20795
Description: A more efficient proof of Theorem 5.3 of [Clemente] p. 16. Compare with ex-natded5.3 20794 and ex-natded5.3i 20796. (Contributed by Mario Carneiro, 9-Feb-2017.)
Hypotheses
Ref Expression
ex-natded5.3.1  |-  ( ph  ->  ( ps  ->  ch ) )
ex-natded5.3.2  |-  ( ph  ->  ( ch  ->  th )
)
Assertion
Ref Expression
ex-natded5.3-2  |-  ( ph  ->  ( ps  ->  ( ch  /\  th ) ) )

Proof of Theorem ex-natded5.3-2
StepHypRef Expression
1 ex-natded5.3.1 . 2  |-  ( ph  ->  ( ps  ->  ch ) )
2 ex-natded5.3.2 . . 3  |-  ( ph  ->  ( ch  ->  th )
)
31, 2syld 40 . 2  |-  ( ph  ->  ( ps  ->  th )
)
41, 3jcad 519 1  |-  ( ph  ->  ( ps  ->  ( ch  /\  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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