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Theorem difeq12 3380
 Description: Equality theorem for class difference. (Contributed by FL, 31-Aug-2009.)
Assertion
Ref Expression
difeq12 ((A = B C = D) → (A C) = (B D))

Proof of Theorem difeq12
StepHypRef Expression
1 difeq1 3246 . 2 (A = B → (A C) = (B C))
2 difeq2 3247 . 2 (C = D → (B C) = (B D))
31, 2sylan9eq 2405 1 ((A = B C = D) → (A C) = (B D))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∧ wa 358   = wceq 1642   ∖ cdif 3206 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  df-compl 3212  df-in 3213  df-dif 3215 This theorem is referenced by:  resdif  5306
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