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Theorem difeq12i 4083
 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 4081 . 2 (𝐴𝐶) = (𝐵𝐶)
3 difeq12i.2 . . 3 𝐶 = 𝐷
43difeq2i 4082 . 2 (𝐵𝐶) = (𝐵𝐷)
52, 4eqtri 2847 1 (𝐴𝐶) = (𝐵𝐷)
 Colors of variables: wff setvar class Syntax hints:   = wceq 1538   ∖ cdif 3916 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1912  ax-6 1971  ax-7 2016  ax-8 2117  ax-9 2125  ax-ext 2796 This theorem depends on definitions:  df-bi 210  df-an 400  df-ex 1782  df-sb 2071  df-clab 2803  df-cleq 2817  df-clel 2896  df-rab 3142  df-dif 3922 This theorem is referenced by:  difrab  4262  preddif  6160  infdju1  9613  uniioombllem4  24197  clwwlknclwwlkdif  27771  gtiso  30451  satffunlem2lem2  32714  mthmpps  32890  zrdivrng  35340  isdrngo1  35343  pwfi2f1o  39961  salexct2  42910  dfnelbr2  43760
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