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Theorem difeq12i 3710
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 (𝐴𝐶) = (𝐵𝐷)

Proof of Theorem difeq12i
StepHypRef Expression
1 difeq1i.1 . . 3 𝐴 = 𝐵
21difeq1i 3708 . 2 (𝐴𝐶) = (𝐵𝐶)
3 difeq12i.2 . . 3 𝐶 = 𝐷
43difeq2i 3709 . 2 (𝐵𝐶) = (𝐵𝐷)
52, 4eqtri 2643 1 (𝐴𝐶) = (𝐵𝐷)
Colors of variables: wff setvar class
Syntax hints:   = wceq 1480  cdif 3557
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1719  ax-4 1734  ax-5 1836  ax-6 1885  ax-7 1932  ax-9 1996  ax-10 2016  ax-11 2031  ax-12 2044  ax-13 2245  ax-ext 2601
This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-tru 1483  df-ex 1702  df-nf 1707  df-sb 1878  df-clab 2608  df-cleq 2614  df-clel 2617  df-nfc 2750  df-ral 2913  df-rab 2917  df-dif 3563
This theorem is referenced by:  difrab  3883  preddif  5674  uniioombllem4  23294  gtiso  29362  mthmpps  31240  zrdivrng  33423  isdrngo1  33426  pwfi2f1o  37185  salexct2  39894
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