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Theorem rneq 4956
 Description: Equality theorem for range. (Contributed by set.mm contributors, 29-Dec-1996.)
Assertion
Ref Expression
rneq (A = B → ran A = ran B)

Proof of Theorem rneq
StepHypRef Expression
1 imaeq1 4937 . 2 (A = B → (A “ V) = (B “ V))
2 df-rn 4786 . 2 ran A = (A “ V)
3 df-rn 4786 . 2 ran B = (B “ V)
41, 2, 33eqtr4g 2410 1 (A = B → ran A = ran B)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   = wceq 1642  Vcvv 2859   “ cima 4722  ran crn 4773 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  df-rn 4786 This theorem is referenced by:  rneqi  4957  rneqd  4958  feq1  5210  foeq1  5265  fconst5  5455  fvranfn  5869  map0e  6023  1cnc  6139  frecxpg  6315
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