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Theorem necon1i 2814
Description: Contrapositive inference for inequality. (Contributed by NM, 18-Mar-2007.)
Hypothesis
Ref Expression
necon1i.1 (𝐴𝐵𝐶 = 𝐷)
Assertion
Ref Expression
necon1i (𝐶𝐷𝐴 = 𝐵)

Proof of Theorem necon1i
StepHypRef Expression
1 df-ne 2781 . . 3 (𝐴𝐵 ↔ ¬ 𝐴 = 𝐵)
2 necon1i.1 . . 3 (𝐴𝐵𝐶 = 𝐷)
31, 2sylbir 223 . 2 𝐴 = 𝐵𝐶 = 𝐷)
43necon1ai 2808 1 (𝐶𝐷𝐴 = 𝐵)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4   = wceq 1474  wne 2779
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 195  df-ne 2781
This theorem is referenced by: (None)
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