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Theorem imaeq1i 4939
 Description: Equality theorem for image. (Contributed by set.mm contributors, 21-Dec-2008.)
Hypothesis
Ref Expression
imaeq1i.1 A = B
Assertion
Ref Expression
imaeq1i (AC) = (BC)

Proof of Theorem imaeq1i
StepHypRef Expression
1 imaeq1i.1 . 2 A = B
2 imaeq1 4937 . 2 (A = B → (AC) = (BC))
31, 2ax-mp 8 1 (AC) = (BC)
 Colors of variables: wff setvar class Syntax hints:   = wceq 1642   “ cima 4722 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-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:  mptpreima  5682
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