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Theorem pm2.61iine 2789
Description: Equality version of pm2.61ii 165. (Contributed by Scott Fenton, 13-Jun-2013.) (Proof shortened by Wolf Lammen, 25-Nov-2019.)
Hypotheses
Ref Expression
pm2.61iine.1  |-  ( ( A  =/=  C  /\  B  =/=  D )  ->  ph )
pm2.61iine.2  |-  ( A  =  C  ->  ph )
pm2.61iine.3  |-  ( B  =  D  ->  ph )
Assertion
Ref Expression
pm2.61iine  |-  ph

Proof of Theorem pm2.61iine
StepHypRef Expression
1 pm2.61iine.2 . 2  |-  ( A  =  C  ->  ph )
2 pm2.61iine.3 . . . 4  |-  ( B  =  D  ->  ph )
32adantl 466 . . 3  |-  ( ( A  =/=  C  /\  B  =  D )  ->  ph )
4 pm2.61iine.1 . . 3  |-  ( ( A  =/=  C  /\  B  =/=  D )  ->  ph )
53, 4pm2.61dane 2785 . 2  |-  ( A  =/=  C  ->  ph )
61, 5pm2.61ine 2780 1  |-  ph
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    /\ wa 369    = wceq 1379    =/= wne 2662
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-an 371  df-ne 2664
This theorem is referenced by:  dedekind  9743
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