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Theorem ex-natded5.7-2 20799
Description: A more efficient proof of Theorem 5.7 of [Clemente] p. 19. Compare with ex-natded5.7 20798. (Contributed by Mario Carneiro, 9-Feb-2017.)
Hypothesis
Ref Expression
ex-natded5.7.1  |-  ( ph  ->  ( ps  \/  ( ch  /\  th ) ) )
Assertion
Ref Expression
ex-natded5.7-2  |-  ( ph  ->  ( ps  \/  ch ) )

Proof of Theorem ex-natded5.7-2
StepHypRef Expression
1 ex-natded5.7.1 . 2  |-  ( ph  ->  ( ps  \/  ( ch  /\  th ) ) )
2 simpl 443 . . 3  |-  ( ( ch  /\  th )  ->  ch )
32orim2i 504 . 2  |-  ( ( ps  \/  ( ch 
/\  th ) )  -> 
( ps  \/  ch ) )
41, 3syl 15 1  |-  ( ph  ->  ( ps  \/  ch ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    \/ wo 357    /\ 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-or 359  df-an 360
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