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Theorem neeqtrrd 2377
Description: Substitution of equal classes into an inequality. (Contributed by NM, 4-Jul-2012.)
Hypotheses
Ref Expression
neeqtrrd.1 (𝜑𝐴𝐵)
neeqtrrd.2 (𝜑𝐶 = 𝐵)
Assertion
Ref Expression
neeqtrrd (𝜑𝐴𝐶)

Proof of Theorem neeqtrrd
StepHypRef Expression
1 neeqtrrd.1 . 2 (𝜑𝐴𝐵)
2 neeqtrrd.2 . . 3 (𝜑𝐶 = 𝐵)
32eqcomd 2183 . 2 (𝜑𝐵 = 𝐶)
41, 3neeqtrd 2375 1 (𝜑𝐴𝐶)
Colors of variables: wff set class
Syntax hints:  wi 4   = wceq 1353  wne 2347
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-in1 614  ax-in2 615  ax-5 1447  ax-gen 1449  ax-4 1510  ax-17 1526  ax-ext 2159
This theorem depends on definitions:  df-bi 117  df-cleq 2170  df-ne 2348
This theorem is referenced by:  frecabcl  6400  expnprm  12351
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