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Theorem nonconne 2659
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 pm3.24 877 . 2  |-  -.  ( A  =  B  /\  -.  A  =  B
)
2 df-ne 2649 . . 3  |-  ( A  =/=  B  <->  -.  A  =  B )
32anbi2i 694 . 2  |-  ( ( A  =  B  /\  A  =/=  B )  <->  ( A  =  B  /\  -.  A  =  B ) )
41, 3mtbir 299 1  |-  -.  ( A  =  B  /\  A  =/=  B )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    /\ wa 369    = wceq 1370    =/= wne 2647
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 2649
This theorem is referenced by:  osumcllem11N  33933  pexmidlem8N  33944  dochexmidlem8  35435
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