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Theorem rneqi 4957
 Description: Equality inference for range. (Contributed by set.mm contributors, 4-Mar-2004.)
Hypothesis
Ref Expression
rneqi.1 A = B
Assertion
Ref Expression
rneqi ran A = ran B

Proof of Theorem rneqi
StepHypRef Expression
1 rneqi.1 . 2 A = B
2 rneq 4956 . 2 (A = B → ran A = ran B)
31, 2ax-mp 8 1 ran A = ran B
 Colors of variables: wff setvar class Syntax hints:   = wceq 1642  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:  resima  5006  resima2  5007  ima0  5013  imaundi  5039  imaundir  5040  dminxp  5061  imadmres  5079  dmco  5089  resdif  5306  fpr  5437  rnoprab  5576  mptpreima  5682  rnmpt  5686  rnmpt2  5717
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