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Theorem nfne 2610
 Description: Bound-variable hypothesis builder for inequality. (Contributed by NM, 10-Nov-2007.) (Revised by Mario Carneiro, 7-Oct-2016.)
Hypotheses
Ref Expression
nfne.1 xA
nfne.2 xB
Assertion
Ref Expression
nfne x AB

Proof of Theorem nfne
StepHypRef Expression
1 df-ne 2518 . 2 (AB ↔ ¬ A = B)
2 nfne.1 . . . 4 xA
3 nfne.2 . . . 4 xB
42, 3nfeq 2496 . . 3 x A = B
54nfn 1793 . 2 x ¬ A = B
61, 5nfxfr 1570 1 x AB
 Colors of variables: wff setvar class Syntax hints:  ¬ wn 3  Ⅎwnf 1544   = wceq 1642  Ⅎwnfc 2476   ≠ wne 2516 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-cleq 2346  df-clel 2349  df-nfc 2478  df-ne 2518 This theorem is referenced by: (None)
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