Theorem rneqi 3340

Description: Equality inference for range.

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 3339	. 2 |- (A = B -> ran A = ran B)
3	1, 2	ax-mp 7	1 |- ran A = ran B

Syntax hints:   = wceq 956  ran crn 3171

This theorem is referenced by:  resima 3391  ima0 3420  imaun 3460  imaun2 3461  dminxp 3483  rnresv 3491  imacnvcnv 3495  imadmres 3498  dmco2 3504  fopab2 3823  rnoprab 4004  curry1 4098  xpassen 4441  sbthlem6 4452  unfilem1 4548  ac6lem 4754  subtop 7646  bafval 8223  cnnvba 8309  dfrelog 8756  pjrn 9647  ghomsn 10388  cayleylem2 10410  cmpran 10469  bsi 10495  rdmob 10681

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 962  ax-gen 963  ax-8 964  ax-10 966  ax-11 967  ax-12 968  ax-13 969  ax-14 970  ax-17 971  ax-4 973  ax-5o 975  ax-6o 978  ax-9o 1123  ax-10o 1140  ax-16 1210  ax-11o 1218  ax-ext 1459  ax-sep 2703  ax-pow 2742  ax-pr 2779

This theorem depends on definitions:  df-bi 147  df-or 224  df-an 225  df-ex 981  df-sb 1172  df-eu 1382  df-mo 1383  df-clab 1464  df-cleq 1469  df-clel 1472  df-ne 1587  df-v 1812  df-dif 2049  df-un 2050  df-in 2051  df-ss 2053  df-nul 2281  df-pw 2402  df-sn 2412  df-pr 2413  df-op 2416  df-br 2620  df-opab 2667  df-cnv 3186  df-dm 3188  df-rn 3189

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