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Theorem nineq2 3235
Description: Equality law for anti-intersection. (Contributed by SF, 11-Jan-2015.)
Assertion
Ref Expression
nineq2 (A = B → (CA) = (CB))

Proof of Theorem nineq2
StepHypRef Expression
1 nineq1 3234 . 2 (A = B → (AC) = (BC))
2 nincom 3226 . 2 (AC) = (CA)
3 nincom 3226 . 2 (BC) = (CB)
41, 2, 33eqtr3g 2408 1 (A = B → (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:  nineq12  3236  nineq2i  3238  nineq2d  3241  ninexg  4097
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