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Theorem imaeq1d 4941
 Description: Equality theorem for image. (Contributed by FL, 15-Dec-2006.)
Hypothesis
Ref Expression
imaeq1d.1 (φA = B)
Assertion
Ref Expression
imaeq1d (φ → (AC) = (BC))

Proof of Theorem imaeq1d
StepHypRef Expression
1 imaeq1d.1 . 2 (φA = B)
2 imaeq1 4937 . 2 (A = B → (AC) = (BC))
31, 2syl 15 1 (φ → (AC) = (BC))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   = wceq 1642   “ cima 4722 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 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-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-rex 2620  df-br 4640  df-ima 4727 This theorem is referenced by:  imaeq12d  4943  nfimad  4954  foimacnv  5303  enprmaplem3  6078  enprmaplem5  6080  enprmaplem6  6081
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