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Theorem neeqtrrd 2229
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 2042 . 2 (φB = 𝐶)
41, 3neeqtrd 2227 1 (φA𝐶)
Colors of variables: wff set class
Syntax hints:  wi 4   = wceq 1242  wne 2201
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in1 544  ax-in2 545  ax-5 1333  ax-gen 1335  ax-4 1397  ax-17 1416  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-cleq 2030  df-ne 2203
This theorem is referenced by: (None)
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