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Theorem necon3bii 2284
Description: Inference from equality to inequality. (Contributed by NM, 23-Feb-2005.)
Hypothesis
Ref Expression
necon3bii.1  |-  ( A  =  B  <->  C  =  D )
Assertion
Ref Expression
necon3bii  |-  ( A  =/=  B  <->  C  =/=  D )

Proof of Theorem necon3bii
StepHypRef Expression
1 necon3bii.1 . . 3  |-  ( A  =  B  <->  C  =  D )
21necon3abii 2282 . 2  |-  ( A  =/=  B  <->  -.  C  =  D )
3 df-ne 2247 . 2  |-  ( C  =/=  D  <->  -.  C  =  D )
42, 3bitr4i 185 1  |-  ( A  =/=  B  <->  C  =/=  D )
Colors of variables: wff set class
Syntax hints:   -. wn 3    <-> wb 103    = wceq 1285    =/= wne 2246
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-in1 577  ax-in2 578
This theorem depends on definitions:  df-bi 115  df-ne 2247
This theorem is referenced by:  necom  2330  negne0bi  7448
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