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Theorem difeq1d 3384
 Description: Deduction adding difference to the right in a class equality. (Contributed by NM, 15-Nov-2002.)
Hypothesis
Ref Expression
difeq1d.1 (φA = B)
Assertion
Ref Expression
difeq1d (φ → (A C) = (B C))

Proof of Theorem difeq1d
StepHypRef Expression
1 difeq1d.1 . 2 (φA = B)
2 difeq1 3246 . 2 (A = B → (A C) = (B C))
31, 2syl 15 1 (φ → (A C) = (B C))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   = 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:  difeq12d  3386  diftpsn3  3849  ssfin  4470  enadj  6060
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