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Theorem ornld 896
Description: Selecting one statement from a disjunction if one of the disjuncted statements is false. (Contributed by AV, 6-Sep-2018.) (Proof shortened by AV, 13-Oct-2018.) (Proof shortened by Wolf Lammen, 19-Jan-2020.)
Assertion
Ref Expression
ornld  |-  ( ph  ->  ( ( ( ph  ->  ( th  \/  ta ) )  /\  -.  th )  ->  ta )
)

Proof of Theorem ornld
StepHypRef Expression
1 pm3.35 587 . . 3  |-  ( (
ph  /\  ( ph  ->  ( th  \/  ta ) ) )  -> 
( th  \/  ta ) )
21ord 377 . 2  |-  ( (
ph  /\  ( ph  ->  ( th  \/  ta ) ) )  -> 
( -.  th  ->  ta ) )
32expimpd 603 1  |-  ( ph  ->  ( ( ( ph  ->  ( th  \/  ta ) )  /\  -.  th )  ->  ta )
)
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    -> wi 4    \/ wo 368    /\ wa 369
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371
This theorem is referenced by:  friendshipgt3  24986  ralralimp  32129
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