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Theorem neeqtri 2729
Description: Substitution of equal classes into an inequality. (Contributed by NM, 4-Jul-2012.)
Hypotheses
Ref Expression
neeqtr.1  |-  A  =/= 
B
neeqtr.2  |-  B  =  C
Assertion
Ref Expression
neeqtri  |-  A  =/= 
C

Proof of Theorem neeqtri
StepHypRef Expression
1 neeqtr.1 . 2  |-  A  =/= 
B
2 neeqtr.2 . . 3  |-  B  =  C
32neeq2i 2718 . 2  |-  ( A  =/=  B  <->  A  =/=  C )
41, 3mpbi 211 1  |-  A  =/= 
C
Colors of variables: wff setvar class
Syntax hints:    = wceq 1437    =/= wne 2625
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1665  ax-4 1678  ax-ext 2407
This theorem depends on definitions:  df-bi 188  df-cleq 2421  df-ne 2627
This theorem is referenced by:  neeqtrri  2730
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