NFE Home New Foundations Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  NFE Home  >  Th. List  >  nineq2d GIF version

Theorem nineq2d 3241
Description: Equality deduction for anti-intersection. (Contributed by SF, 11-Jan-2015.)
Hypothesis
Ref Expression
nineqd.1 (φA = B)
Assertion
Ref Expression
nineq2d (φ → (CA) = (CB))

Proof of Theorem nineq2d
StepHypRef Expression
1 nineqd.1 . 2 (φA = B)
2 nineq2 3235 . 2 (A = B → (CA) = (CB))
31, 2syl 15 1 (φ → (CA) = (CB))
Colors of variables: wff setvar class
Syntax hints:  wi 4   = wceq 1642  cnin 3204
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 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-nan 1288  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-v 2861  df-nin 3211
This theorem is referenced by:  difeq2  3247
  Copyright terms: Public domain W3C validator