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Theorem difeq1i 3096
 Description: Inference adding difference to the right in a class equality. (Contributed by NM, 15-Nov-2002.)
Hypothesis
Ref Expression
difeq1i.1 𝐴 = 𝐵
Assertion
Ref Expression
difeq1i (𝐴𝐶) = (𝐵𝐶)

Proof of Theorem difeq1i
StepHypRef Expression
1 difeq1i.1 . 2 𝐴 = 𝐵
2 difeq1 3093 . 2 (𝐴 = 𝐵 → (𝐴𝐶) = (𝐵𝐶))
31, 2ax-mp 7 1 (𝐴𝐶) = (𝐵𝐶)
 Colors of variables: wff set class Syntax hints:   = wceq 1285   ∖ cdif 2979 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2065 This theorem depends on definitions:  df-bi 115  df-tru 1288  df-nf 1391  df-sb 1688  df-clab 2070  df-cleq 2076  df-clel 2079  df-nfc 2212  df-rab 2362  df-dif 2984 This theorem is referenced by:  difeq12i  3098  indif1  3225  indifcom  3226  difun1  3240  notab  3250  notrab  3257  difprsn1  3544  difprsn2  3545  orddif  4318  resdmdfsn  4701  phplem1  6409  dfn2  8438
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