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Theorem neeqtri 3056
Description: Substitution of equal classes into an inequality. (Contributed by NM, 4-Jul-2012.)
Hypotheses
Ref Expression
neeqtr.1 𝐴𝐵
neeqtr.2 𝐵 = 𝐶
Assertion
Ref Expression
neeqtri 𝐴𝐶

Proof of Theorem neeqtri
StepHypRef Expression
1 neeqtr.1 . 2 𝐴𝐵
2 neeqtr.2 . . 3 𝐵 = 𝐶
32neeq2i 3049 . 2 (𝐴𝐵𝐴𝐶)
41, 3mpbi 231 1 𝐴𝐶
Colors of variables: wff setvar class
Syntax hints:   = wceq 1522  wne 2984
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1777  ax-4 1791  ax-5 1888  ax-6 1947  ax-7 1992  ax-9 2091  ax-ext 2769
This theorem depends on definitions:  df-bi 208  df-an 397  df-ex 1762  df-cleq 2788  df-ne 2985
This theorem is referenced by:  neeqtrri  3057
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