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Theorem 3netr4g 3048
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 3035 . 2 (𝐶𝐷𝐴𝐵)
51, 4sylibr 226 1 (𝜑𝐶𝐷)
Colors of variables: wff setvar class
Syntax hints:  wi 4   = wceq 1653  wne 2969
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1891  ax-4 1905  ax-5 2006  ax-6 2072  ax-7 2107  ax-9 2166  ax-ext 2775
This theorem depends on definitions:  df-bi 199  df-an 386  df-ex 1876  df-cleq 2790  df-ne 2970
This theorem is referenced by:  aalioulem2  24425  mapdpglem18  37701
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