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Theorem difeq12i 3160
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 3158 . 2 (𝐴𝐶) = (𝐵𝐶)
3 difeq12i.2 . . 3 𝐶 = 𝐷
43difeq2i 3159 . 2 (𝐵𝐶) = (𝐵𝐷)
52, 4eqtri 2136 1 (𝐴𝐶) = (𝐵𝐷)
Colors of variables: wff set class
Syntax hints:   = wceq 1314  cdif 3036
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 586  ax-in2 587  ax-io 681  ax-5 1406  ax-7 1407  ax-gen 1408  ax-ie1 1452  ax-ie2 1453  ax-8 1465  ax-10 1466  ax-11 1467  ax-i12 1468  ax-bndl 1469  ax-4 1470  ax-17 1489  ax-i9 1493  ax-ial 1497  ax-i5r 1498  ax-ext 2097
This theorem depends on definitions:  df-bi 116  df-tru 1317  df-nf 1420  df-sb 1719  df-clab 2102  df-cleq 2108  df-clel 2111  df-nfc 2245  df-ral 2396  df-rab 2400  df-dif 3041
This theorem is referenced by:  difrab  3318  imadiflem  5170  imadif  5171
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