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Theorem difeq12i 3383
 Description: Equality inference for class difference. (Contributed by NM, 29-Aug-2004.)
Hypotheses
Ref Expression
difeq1i.1 A = B
difeq12i.2 C = D
Assertion
Ref Expression
difeq12i (A C) = (B D)

Proof of Theorem difeq12i
StepHypRef Expression
1 difeq1i.1 . . 3 A = B
21difeq1i 3381 . 2 (A C) = (B C)
3 difeq12i.2 . . 3 C = D
43difeq2i 3382 . 2 (B C) = (B D)
52, 4eqtri 2373 1 (A C) = (B D)
 Colors of variables: wff setvar class Syntax hints:   = 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:  difrab  3529
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