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Theorem 3netr3 25071
Description: Inequality. (Contributed by FL, 30-May-2014.)
Hypotheses
Ref Expression
3netr3.1  |-  A  =/= 
B
3netr3.2  |-  A  =  C
3netr3.3  |-  B  =  D
Assertion
Ref Expression
3netr3  |-  C  =/= 
D

Proof of Theorem 3netr3
StepHypRef Expression
1 3netr3.2 . . 3  |-  A  =  C
2 3netr3.1 . . 3  |-  A  =/= 
B
31, 2eqnetrri 2478 . 2  |-  C  =/= 
B
4 3netr3.3 . 2  |-  B  =  D
53, 4neeqtri 2480 1  |-  C  =/= 
D
Colors of variables: wff set class
Syntax hints:    = wceq 1632    =/= wne 2459
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-11 1727  ax-ext 2277
This theorem depends on definitions:  df-bi 177  df-cleq 2289  df-ne 2461
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