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Theorem necon3i 2268
Description: Contrapositive inference for inequality. (Contributed by NM, 9-Aug-2006.)
Hypothesis
Ref Expression
necon3i.1 (𝐴 = 𝐵𝐶 = 𝐷)
Assertion
Ref Expression
necon3i (𝐶𝐷𝐴𝐵)

Proof of Theorem necon3i
StepHypRef Expression
1 necon3i.1 . 2 (𝐴 = 𝐵𝐶 = 𝐷)
2 id 19 . . 3 ((𝐴 = 𝐵𝐶 = 𝐷) → (𝐴 = 𝐵𝐶 = 𝐷))
32necon3d 2264 . 2 ((𝐴 = 𝐵𝐶 = 𝐷) → (𝐶𝐷𝐴𝐵))
41, 3ax-mp 7 1 (𝐶𝐷𝐴𝐵)
Colors of variables: wff set class
Syntax hints:  wi 4   = wceq 1259  wne 2220
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-in1 554  ax-in2 555
This theorem depends on definitions:  df-bi 114  df-ne 2221
This theorem is referenced by: (None)
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