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Theorem nineq12 3236
 Description: Equality law for anti-intersection. (Contributed by SF, 11-Jan-2015.)
Assertion
Ref Expression
nineq12 ((A = B C = D) → (AC) = (BD))

Proof of Theorem nineq12
StepHypRef Expression
1 nineq1 3234 . 2 (A = B → (AC) = (BC))
2 nineq2 3235 . 2 (C = D → (BC) = (BD))
31, 2sylan9eq 2405 1 ((A = B C = D) → (AC) = (BD))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∧ wa 358   = wceq 1642   ⩃ cnin 3204 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-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:  nineq12i  3239  nineq12d  3242  compleq  3243
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