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Theorem difeq2i 3161
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 3158 . 2 (𝐴 = 𝐵 → (𝐶𝐴) = (𝐶𝐵))
31, 2ax-mp 5 1 (𝐶𝐴) = (𝐶𝐵)
Colors of variables: wff set class
Syntax hints:   = wceq 1316  cdif 3038
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 588  ax-in2 589  ax-5 1408  ax-7 1409  ax-gen 1410  ax-ie1 1454  ax-ie2 1455  ax-8 1467  ax-11 1469  ax-4 1472  ax-17 1491  ax-i9 1495  ax-ial 1499  ax-i5r 1500  ax-ext 2099
This theorem depends on definitions:  df-bi 116  df-tru 1319  df-nf 1422  df-sb 1721  df-clab 2104  df-cleq 2110  df-clel 2113  df-ral 2398  df-rab 2402  df-dif 3043
This theorem is referenced by:  difeq12i  3162  inssddif  3287  difdif2ss  3303  dif32  3309  difabs  3310  symdif1  3311  notrab  3323  dif0  3403  difdifdirss  3417  dfif3  3457  difpr  3632  dif1o  6303  unfiin  6782
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