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Theorem difeq12i 4120
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 4118 . 2 (𝐴𝐶) = (𝐵𝐶)
3 difeq12i.2 . . 3 𝐶 = 𝐷
43difeq2i 4119 . 2 (𝐵𝐶) = (𝐵𝐷)
52, 4eqtri 2759 1 (𝐴𝐶) = (𝐵𝐷)
Colors of variables: wff setvar class
Syntax hints:   = wceq 1540  cdif 3945
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1912  ax-6 1970  ax-7 2010  ax-8 2107  ax-9 2115  ax-ext 2702
This theorem depends on definitions:  df-bi 206  df-an 396  df-ex 1781  df-sb 2067  df-clab 2709  df-cleq 2723  df-clel 2809  df-rab 3432  df-dif 3951
This theorem is referenced by:  indifdir  4284  difrab  4308  resdifdi  6235  resdifdir  6236  preddif  6330  infdju1  10187  uniioombllem4  25336  new0  27607  clwwlknclwwlkdif  29500  gtiso  32190  satffunlem2lem2  34696  mthmpps  34872  zrdivrng  37125  isdrngo1  37128  pwfi2f1o  42141  salexct2  45354  dfnelbr2  46280
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