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Theorem difeq1i 3381
 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 (A C) = (B C)

Proof of Theorem difeq1i
StepHypRef Expression
1 difeq1i.1 . 2 A = B
2 difeq1 3246 . 2 (A = B → (A C) = (B C))
31, 2ax-mp 8 1 (A C) = (B C)
 Colors of variables: wff setvar class Syntax hints:   = wceq 1642   ∖ cdif 3206 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-nan 1288  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-v 2861  df-nin 3211  df-compl 3212  df-in 3213  df-dif 3215 This theorem is referenced by:  difeq12i  3383  dfin3  3494  indif1  3499  indifcom  3500  difun1  3514  notab  3525  notrab  3532  undifabs  3627  difprsn1  3847  difprsn2  3848
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