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Theorem ex-natded5.7-2 20752
Description: A more efficient proof of Theorem 5.7 of [Laboreo] p. 19. Compare with ex-natded5.7 20751. (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 445 . . 3  |-  ( ( ch  /\  th )  ->  ch )
32orim2i 506 . 2  |-  ( ( ps  \/  ( ch 
/\  th ) )  -> 
( ps  \/  ch ) )
41, 3syl 17 1  |-  ( ph  ->  ( ps  \/  ch ) )
Colors of variables: wff set class
Syntax hints:    -> wi 6    \/ wo 359    /\ 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-or 361  df-an 362
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