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Theorem nonconne 2346
Description: Law of noncontradiction with equality and inequality. (Contributed by NM, 3-Feb-2012.)
Assertion
Ref Expression
nonconne  |-  -.  ( A  =  B  /\  A  =/=  B )

Proof of Theorem nonconne
StepHypRef Expression
1 pm3.24 683 . 2  |-  -.  ( A  =  B  /\  -.  A  =  B
)
2 df-ne 2335 . . 3  |-  ( A  =/=  B  <->  -.  A  =  B )
32anbi2i 453 . 2  |-  ( ( A  =  B  /\  A  =/=  B )  <->  ( A  =  B  /\  -.  A  =  B ) )
41, 3mtbir 661 1  |-  -.  ( A  =  B  /\  A  =/=  B )
Colors of variables: wff set class
Syntax hints:   -. wn 3    /\ wa 103    = wceq 1342    =/= wne 2334
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 604  ax-in2 605
This theorem depends on definitions:  df-bi 116  df-ne 2335
This theorem is referenced by: (None)
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