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Theorem 3netr4g 2320
Description: Substitution of equality into both sides of an inequality. (Contributed by NM, 14-Jun-2012.)
Hypotheses
Ref Expression
3netr4g.1 (𝜑𝐴𝐵)
3netr4g.2 𝐶 = 𝐴
3netr4g.3 𝐷 = 𝐵
Assertion
Ref Expression
3netr4g (𝜑𝐶𝐷)

Proof of Theorem 3netr4g
StepHypRef Expression
1 3netr4g.1 . 2 (𝜑𝐴𝐵)
2 3netr4g.2 . . 3 𝐶 = 𝐴
3 3netr4g.3 . . 3 𝐷 = 𝐵
42, 3neeq12i 2302 . 2 (𝐶𝐷𝐴𝐵)
51, 4sylibr 133 1 (𝜑𝐶𝐷)
Colors of variables: wff set class
Syntax hints:  wi 4   = wceq 1316  wne 2285
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 588  ax-in2 589  ax-5 1408  ax-gen 1410  ax-4 1472  ax-17 1491  ax-ext 2099
This theorem depends on definitions:  df-bi 116  df-cleq 2110  df-ne 2286
This theorem is referenced by: (None)
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