Theorem rneqi 4767

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 4766	. 2 |- ( A = B -> ran A = ran B )
3	1, 2	ax-mp 5	1 |- ran A = ran B

Syntax hints:   = wceq 1331   ran crn 4540

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121

This theorem depends on definitions:  df-bi 116  df-3an 964  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2126  df-cleq 2132  df-clel 2135  df-nfc 2270  df-v 2688  df-un 3075  df-in 3077  df-ss 3084  df-sn 3533  df-pr 3534  df-op 3536  df-br 3930  df-opab 3990  df-cnv 4547  df-dm 4549  df-rn 4550

This theorem is referenced by:  rnmpt  4787  resima  4852  resima2  4853  ima0  4898  rnuni  4950  imaundi  4951  imaundir  4952  inimass  4955  dminxp  4983  imainrect  4984  xpima1  4985  xpima2m  4986  rnresv  4998  imacnvcnv  5003  rnpropg  5018  imadmres  5031  mptpreima  5032  dmco  5047  resdif  5389  fpr  5602  fprg  5603  fliftfuns  5699  rnoprab  5854  rnmpo  5881  qliftfuns  6513  xpassen  6724  sbthlemi6  6850  ennnfonelemrn  11932  cnconst2  12402