Theorem rneqi 4894

Description: Equality inference for range. (Contributed by NM, 4-Mar-2004.)

Hypothesis

Ref	Expression
rneqi.1	|- A = B

Assertion

Ref	Expression
rneqi	|- ran A = ran B

Proof of Theorem rneqi

Step	Hyp	Ref	Expression
1		rneqi.1	. 2 |- A = B
2		rneq 4893	. 2 |- ( A = B -> ran A = ran B )
3	1, 2	ax-mp 5	1 |- ran A = ran B

Syntax hints:   = wceq 1364   ran crn 4664

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 710  ax-5 1461  ax-7 1462  ax-gen 1463  ax-ie1 1507  ax-ie2 1508  ax-8 1518  ax-10 1519  ax-11 1520  ax-i12 1521  ax-bndl 1523  ax-4 1524  ax-17 1540  ax-i9 1544  ax-ial 1548  ax-i5r 1549  ax-ext 2178

This theorem depends on definitions:  df-bi 117  df-3an 982  df-tru 1367  df-nf 1475  df-sb 1777  df-clab 2183  df-cleq 2189  df-clel 2192  df-nfc 2328  df-v 2765  df-un 3161  df-in 3163  df-ss 3170  df-sn 3628  df-pr 3629  df-op 3631  df-br 4034  df-opab 4095  df-cnv 4671  df-dm 4673  df-rn 4674

This theorem is referenced by:  rnmpt  4914  resima  4979  resima2  4980  mptima  5021  ima0  5028  rnuni  5081  imaundi  5082  imaundir  5083  inimass  5086  dminxp  5114  imainrect  5115  xpima1  5116  xpima2m  5117  rnresv  5129  imacnvcnv  5134  rnpropg  5149  imadmres  5162  mptpreima  5163  dmco  5178  resdif  5526  fpr  5744  fprg  5745  fliftfuns  5845  rnoprab  6005  rnmpo  6033  qliftfuns  6678  xpassen  6889  sbthlemi6  7028  ennnfonelemrn  12636  cnconst2  14469  elply2  14971