NFE Home New Foundations Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  NFE Home  >  Th. List  >  necon4d GIF version

Theorem necon4d 2579
Description: Contrapositive inference for inequality. (Contributed by NM, 2-Apr-2007.) (Proof shortened by Andrew Salmon, 25-May-2011.)
Hypothesis
Ref Expression
necon4d.1 (φ → (ABCD))
Assertion
Ref Expression
necon4d (φ → (C = DA = B))

Proof of Theorem necon4d
StepHypRef Expression
1 necon4d.1 . . 3 (φ → (ABCD))
21necon2bd 2565 . 2 (φ → (C = D → ¬ AB))
3 nne 2520 . 2 ABA = B)
42, 3syl6ib 217 1 (φ → (C = DA = B))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4   = wceq 1642  wne 2516
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 177  df-ne 2518
This theorem is referenced by:  tfin11  4493
  Copyright terms: Public domain W3C validator