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Theorem difeq12d 3386
Description: Equality deduction for class difference. (Contributed by FL, 29-May-2014.)
Hypotheses
Ref Expression
difeq12d.1 (φA = B)
difeq12d.2 (φC = D)
Assertion
Ref Expression
difeq12d (φ → (A C) = (B D))

Proof of Theorem difeq12d
StepHypRef Expression
1 difeq12d.1 . . 3 (φA = B)
21difeq1d 3384 . 2 (φ → (A C) = (B C))
3 difeq12d.2 . . 3 (φC = D)
43difeq2d 3385 . 2 (φ → (B C) = (B D))
52, 4eqtrd 2385 1 (φ → (A C) = (B D))
Colors of variables: wff setvar class
Syntax hints:  wi 4   = 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:  nnsucelr  4428
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