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Theorem necon2i 2976
Description: Contrapositive inference for inequality. (Contributed by NM, 18-Mar-2007.)
Hypothesis
Ref Expression
necon2i.1 (𝐴 = 𝐵𝐶𝐷)
Assertion
Ref Expression
necon2i (𝐶 = 𝐷𝐴𝐵)

Proof of Theorem necon2i
StepHypRef Expression
1 necon2i.1 . . 3 (𝐴 = 𝐵𝐶𝐷)
21neneqd 2947 . 2 (𝐴 = 𝐵 → ¬ 𝐶 = 𝐷)
32necon2ai 2971 1 (𝐶 = 𝐷𝐴𝐵)
Colors of variables: wff setvar class
Syntax hints:  wi 4   = wceq 1630  wne 2942
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 197  df-ne 2943
This theorem is referenced by:  cmpfi  21431  mcubic  24794  cubic2  24795  2sqlem11  25374  ovoliunnfl  33777  voliunnfl  33779  volsupnfl  33780  mncn0  38228  aaitgo  38251
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