Theorem rneqi 4505

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 4504	. 2 |- (A = B -> ran A = ran B)
3	1, 2	ax-mp 7	1 |- ran A = ran B

Syntax hints:   = wceq 1242   ran crn 4289

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bndl 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019

This theorem depends on definitions:  df-bi 110  df-3an 886  df-tru 1245  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-v 2553  df-un 2916  df-in 2918  df-ss 2925  df-sn 3373  df-pr 3374  df-op 3376  df-br 3756  df-opab 3810  df-cnv 4296  df-dm 4298  df-rn 4299

This theorem is referenced by:  rnmpt  4525  resima  4586  resima2  4587  ima0  4627  rnuni  4678  imaundi  4679  imaundir  4680  inimass  4683  dminxp  4708  imainrect  4709  xpima1  4710  xpima2m  4711  rnresv  4723  imacnvcnv  4728  rnpropg  4743  imadmres  4756  mptpreima  4757  dmco  4772  resdif  5091  fpr  5288  fprg  5289  fliftfuns  5381  rnoprab  5529  rnmpt2  5553  qliftfuns  6126  xpassen  6240