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Theorem 3netr4g 2775
Description: Substitution of equality into both sides of an inequality. (Contributed by NM, 14-Jun-2012.)
Hypotheses
Ref Expression
3netr4g.1  |-  ( ph  ->  A  =/=  B )
3netr4g.2  |-  C  =  A
3netr4g.3  |-  D  =  B
Assertion
Ref Expression
3netr4g  |-  ( ph  ->  C  =/=  D )

Proof of Theorem 3netr4g
StepHypRef Expression
1 3netr4g.1 . 2  |-  ( ph  ->  A  =/=  B )
2 3netr4g.2 . . 3  |-  C  =  A
3 3netr4g.3 . . 3  |-  D  =  B
42, 3neeq12i 2756 . 2  |-  ( C  =/=  D  <->  A  =/=  B )
51, 4sylibr 212 1  |-  ( ph  ->  C  =/=  D )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    = wceq 1379    =/= wne 2662
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1601  ax-4 1612  ax-ext 2445
This theorem depends on definitions:  df-bi 185  df-cleq 2459  df-ne 2664
This theorem is referenced by:  aalioulem2  22596  mapdpglem18  36887
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