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Theorem ex-natded5.3-2 20653
Description: A more efficient proof of Theorem 5.3 of [Laboreo] p. 16. Compare with ex-natded5.3 20652 and ex-natded5.3i 20654. (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 42 . 2  |-  ( ph  ->  ( ps  ->  th )
)
41, 3jcad 521 1  |-  ( ph  ->  ( ps  ->  ( ch  /\  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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