Theorem rneqi 4925

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 4924	. 2 |- ( A = B -> ran A = ran B )
3	1, 2	ax-mp 5	1 |- ran A = ran B

Syntax hints:   = wceq 1373   ran crn 4694

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 711  ax-5 1471  ax-7 1472  ax-gen 1473  ax-ie1 1517  ax-ie2 1518  ax-8 1528  ax-10 1529  ax-11 1530  ax-i12 1531  ax-bndl 1533  ax-4 1534  ax-17 1550  ax-i9 1554  ax-ial 1558  ax-i5r 1559  ax-ext 2189

This theorem depends on definitions:  df-bi 117  df-3an 983  df-tru 1376  df-nf 1485  df-sb 1787  df-clab 2194  df-cleq 2200  df-clel 2203  df-nfc 2339  df-v 2778  df-un 3178  df-in 3180  df-ss 3187  df-sn 3649  df-pr 3650  df-op 3652  df-br 4060  df-opab 4122  df-cnv 4701  df-dm 4703  df-rn 4704

This theorem is referenced by:  rnmpt  4945  resima  5011  resima2  5012  mptima  5053  ima0  5060  rnuni  5113  imaundi  5114  imaundir  5115  inimass  5118  dminxp  5146  imainrect  5147  xpima1  5148  xpima2m  5149  rnresv  5161  imacnvcnv  5166  rnpropg  5181  imadmres  5194  mptpreima  5195  dmco  5210  resdif  5566  fpr  5789  fprg  5790  fliftfuns  5890  rnoprab  6051  rnmpo  6079  qliftfuns  6729  xpassen  6950  sbthlemi6  7090  ennnfonelemrn  12905  cnconst2  14820  elply2  15322  iedgedgg  15772  edgiedgbg  15776  edg0iedg0g  15777  uhgrvtxedgiedgb  15847