Theorem rneqi 4590

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 4589	. 2 |- ( A = B -> ran A = ran B )
3	1, 2	ax-mp 7	1 |- ran A = ran B

Syntax hints:   = wceq 1285   ran crn 4372

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2064

This theorem depends on definitions:  df-bi 115  df-3an 922  df-tru 1288  df-nf 1391  df-sb 1687  df-clab 2069  df-cleq 2075  df-clel 2078  df-nfc 2209  df-v 2604  df-un 2978  df-in 2980  df-ss 2987  df-sn 3412  df-pr 3413  df-op 3415  df-br 3794  df-opab 3848  df-cnv 4379  df-dm 4381  df-rn 4382

This theorem is referenced by:  rnmpt  4610  resima  4671  resima2  4672  ima0  4714  rnuni  4765  imaundi  4766  imaundir  4767  inimass  4770  dminxp  4795  imainrect  4796  xpima1  4797  xpima2m  4798  rnresv  4810  imacnvcnv  4815  rnpropg  4830  imadmres  4843  mptpreima  4844  dmco  4859  resdif  5179  fpr  5377  fprg  5378  fliftfuns  5469  rnoprab  5618  rnmpt2  5642  qliftfuns  6256  xpassen  6374