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Theorem difeq12i 4123
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 4121 . 2 (𝐴𝐶) = (𝐵𝐶)
3 difeq12i.2 . . 3 𝐶 = 𝐷
43difeq2i 4122 . 2 (𝐵𝐶) = (𝐵𝐷)
52, 4eqtri 2764 1 (𝐴𝐶) = (𝐵𝐷)
Colors of variables: wff setvar class
Syntax hints:   = wceq 1539  cdif 3947
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1794  ax-4 1808  ax-5 1909  ax-6 1966  ax-7 2006  ax-8 2109  ax-9 2117  ax-ext 2707
This theorem depends on definitions:  df-bi 207  df-an 396  df-ex 1779  df-sb 2064  df-clab 2714  df-cleq 2728  df-clel 2815  df-rab 3436  df-dif 3953
This theorem is referenced by:  indifdir  4294  difrab  4317  resdifdi  6255  resdifdir  6256  preddif  6349  infdju1  10231  uniioombllem4  25622  new0  27914  clwwlknclwwlkdif  29999  gtiso  32711  satffunlem2lem2  35412  mthmpps  35588  zrdivrng  37961  isdrngo1  37964  pwfi2f1o  43113  salexct2  46359  dfnelbr2  47290
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