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Theorem difeq12i 3953
 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 3951 . 2 (𝐴𝐶) = (𝐵𝐶)
3 difeq12i.2 . . 3 𝐶 = 𝐷
43difeq2i 3952 . 2 (𝐵𝐶) = (𝐵𝐷)
52, 4eqtri 2849 1 (𝐴𝐶) = (𝐵𝐷)
 Colors of variables: wff setvar class Syntax hints:   = wceq 1656   ∖ cdif 3795 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1894  ax-4 1908  ax-5 2009  ax-6 2075  ax-7 2112  ax-9 2173  ax-10 2192  ax-11 2207  ax-12 2220  ax-ext 2803 This theorem depends on definitions:  df-bi 199  df-an 387  df-or 879  df-tru 1660  df-ex 1879  df-nf 1883  df-sb 2068  df-clab 2812  df-cleq 2818  df-clel 2821  df-nfc 2958  df-ral 3122  df-rab 3126  df-dif 3801 This theorem is referenced by:  difrab  4130  preddif  5945  uniioombllem4  23752  clwwlknclwwlkdif  27308  gtiso  30015  mthmpps  32014  zrdivrng  34287  isdrngo1  34290  pwfi2f1o  38502  salexct2  41341  dfnelbr2  42168
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