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Theorem difeq2i 3036
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 3033 . 2 (A = B → (𝐶A) = (𝐶B))
31, 2ax-mp 7 1 (𝐶A) = (𝐶B)
Colors of variables: wff set class
Syntax hints:   = wceq 1228  cdif 2891
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in1 532  ax-in2 533  ax-5 1316  ax-7 1317  ax-gen 1318  ax-ie1 1363  ax-ie2 1364  ax-8 1376  ax-11 1378  ax-4 1381  ax-17 1400  ax-i9 1404  ax-ial 1409  ax-i5r 1410  ax-ext 2004
This theorem depends on definitions:  df-bi 110  df-tru 1231  df-nf 1330  df-sb 1628  df-clab 2009  df-cleq 2015  df-clel 2018  df-ral 2289  df-rab 2293  df-dif 2897
This theorem is referenced by:  difeq12i  3037  inssddif  3155  difdif2ss  3171  dif32  3177  difabs  3178  symdif1  3179  notrab  3191  dif0  3271  difdifdirss  3284  dfif3  3320  dif1o  5936
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