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Theorem 3netr4g 2722
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 2709 . 2  |-  ( C  =/=  D  <->  A  =/=  B )
51, 4sylibr 217 1  |-  ( ph  ->  C  =/=  D )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    = wceq 1452    =/= wne 2641
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1677  ax-4 1690  ax-ext 2451
This theorem depends on definitions:  df-bi 190  df-cleq 2464  df-ne 2643
This theorem is referenced by:  aalioulem2  23368  mapdpglem18  35328
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