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Theorem coeq1d 4878
 Description: Equality deduction for composition of two classes. (Contributed by set.mm contributors, 16-Nov-2000.)
Hypothesis
Ref Expression
coeq1d.1 (φA = B)
Assertion
Ref Expression
coeq1d (φ → (A C) = (B C))

Proof of Theorem coeq1d
StepHypRef Expression
1 coeq1d.1 . 2 (φA = B)
2 coeq1 4874 . 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   ∘ ccom 4721 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-ss 3259  df-opab 4623  df-br 4640  df-co 4726 This theorem is referenced by:  coeq12d  4881  enmap1lem3  6071  enmap1lem5  6073
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