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Theorem difeq2i 3155
Description: Inference adding difference to the left in a class equality. (Contributed by NM, 15-Nov-2002.)
Hypothesis
Ref Expression
difeq1i.1 𝐴 = 𝐵
Assertion
Ref Expression
difeq2i (𝐶𝐴) = (𝐶𝐵)

Proof of Theorem difeq2i
StepHypRef Expression
1 difeq1i.1 . 2 𝐴 = 𝐵
2 difeq2 3152 . 2 (𝐴 = 𝐵 → (𝐶𝐴) = (𝐶𝐵))
31, 2ax-mp 7 1 (𝐶𝐴) = (𝐶𝐵)
Colors of variables: wff set class
Syntax hints:   = wceq 1312  cdif 3032
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 586  ax-in2 587  ax-5 1404  ax-7 1405  ax-gen 1406  ax-ie1 1450  ax-ie2 1451  ax-8 1463  ax-11 1465  ax-4 1468  ax-17 1487  ax-i9 1491  ax-ial 1495  ax-i5r 1496  ax-ext 2095
This theorem depends on definitions:  df-bi 116  df-tru 1315  df-nf 1418  df-sb 1717  df-clab 2100  df-cleq 2106  df-clel 2109  df-ral 2393  df-rab 2397  df-dif 3037
This theorem is referenced by:  difeq12i  3156  inssddif  3281  difdif2ss  3297  dif32  3303  difabs  3304  symdif1  3305  notrab  3317  dif0  3397  difdifdirss  3411  dfif3  3451  difpr  3626  dif1o  6287  unfiin  6765
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