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Theorem difeq12i 4119
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 4117 . 2 (𝐴𝐶) = (𝐵𝐶)
3 difeq12i.2 . . 3 𝐶 = 𝐷
43difeq2i 4118 . 2 (𝐵𝐶) = (𝐵𝐷)
52, 4eqtri 2758 1 (𝐴𝐶) = (𝐵𝐷)
Colors of variables: wff setvar class
Syntax hints:   = wceq 1539  cdif 3944
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1911  ax-6 1969  ax-7 2009  ax-8 2106  ax-9 2114  ax-ext 2701
This theorem depends on definitions:  df-bi 206  df-an 395  df-ex 1780  df-sb 2066  df-clab 2708  df-cleq 2722  df-clel 2808  df-rab 3431  df-dif 3950
This theorem is referenced by:  indifdir  4283  difrab  4307  resdifdi  6234  resdifdir  6235  preddif  6329  infdju1  10186  uniioombllem4  25335  new0  27606  clwwlknclwwlkdif  29499  gtiso  32189  satffunlem2lem2  34695  mthmpps  34871  zrdivrng  37124  isdrngo1  37127  pwfi2f1o  42140  salexct2  45353  dfnelbr2  46279
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