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Theorem 3netr4g 3099
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 3086 . 2 (𝐶𝐷𝐴𝐵)
51, 4sylibr 235 1 (𝜑𝐶𝐷)
Colors of variables: wff setvar class
Syntax hints:  wi 4   = wceq 1530  wne 3020
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1904  ax-6 1963  ax-7 2008  ax-9 2116  ax-ext 2796
This theorem depends on definitions:  df-bi 208  df-an 397  df-ex 1774  df-cleq 2817  df-ne 3021
This theorem is referenced by:  aalioulem2  24837  mapdpglem18  38693  line2x  44570
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