Theorem rneqi 3346

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 3345	. 2 |- (A = B -> ran A = ran B)
3	1, 2	ax-mp 7	1 |- ran A = ran B

Syntax hints:   = wceq 958  ran crn 3177

This theorem is referenced by:  resima 3397  ima0 3426  imaun 3466  imaun2 3467  dminxp 3489  rnresv 3497  imacnvcnv 3501  imadmres 3504  dmco2 3510  fopab2 3829  rnoprab 4010  curry1 4104  xpassen 4447  sbthlem6 4458  unfilem1 4560  ac6lem 4764  subtop 7643  bafval 8219  cnnvba 8305  dfrelog 8751  pjrn 9642  ghomsn 10383  cayleylem2 10405  cmpran 10459  bsi 10481  rdmob 10652

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 964  ax-gen 965  ax-8 966  ax-10 968  ax-11 969  ax-12 970  ax-13 971  ax-14 972  ax-17 973  ax-4 975  ax-5o 977  ax-6o 980  ax-9o 1125  ax-10o 1142  ax-16 1212  ax-11o 1220  ax-ext 1462  ax-sep 2708  ax-pow 2748  ax-pr 2785

This theorem depends on definitions:  df-bi 147  df-or 224  df-an 225  df-ex 983  df-sb 1174  df-eu 1384  df-mo 1385  df-clab 1467  df-cleq 1472  df-clel 1475  df-ne 1590  df-v 1815  df-dif 2052  df-un 2053  df-in 2054  df-ss 2056  df-nul 2284  df-pw 2406  df-sn 2416  df-pr 2417  df-op 2420  df-br 2625  df-opab 2672  df-cnv 3192  df-dm 3194  df-rn 3195

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