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Theorem ex-natded5.13-2 20803
Description: A more efficient proof of Theorem 5.13 of [Clemente] p. 20. Compare with ex-natded5.13 20802. (Contributed by Mario Carneiro, 9-Feb-2017.)
Hypotheses
Ref Expression
ex-natded5.13.1  |-  ( ph  ->  ( ps  \/  ch ) )
ex-natded5.13.2  |-  ( ph  ->  ( ps  ->  th )
)
ex-natded5.13.3  |-  ( ph  ->  ( -.  ta  ->  -. 
ch ) )
Assertion
Ref Expression
ex-natded5.13-2  |-  ( ph  ->  ( th  \/  ta ) )

Proof of Theorem ex-natded5.13-2
StepHypRef Expression
1 ex-natded5.13.1 . 2  |-  ( ph  ->  ( ps  \/  ch ) )
2 ex-natded5.13.2 . . 3  |-  ( ph  ->  ( ps  ->  th )
)
3 ex-natded5.13.3 . . . 4  |-  ( ph  ->  ( -.  ta  ->  -. 
ch ) )
43con4d 97 . . 3  |-  ( ph  ->  ( ch  ->  ta ) )
52, 4orim12d 811 . 2  |-  ( ph  ->  ( ( ps  \/  ch )  ->  ( th  \/  ta ) ) )
61, 5mpd 14 1  |-  ( ph  ->  ( th  \/  ta ) )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    \/ wo 357
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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