Theorem rneqi 2556

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 2555	. 2 ⊢ (A = B → ran A = ran B)
3	1, 2	ax-mp 6	1 ⊢ ran A = ran B

Syntax hints:   = wceq 1091  ran crn 2411

This theorem is referenced by:  resima 2595  ima0 2615  imaun 2647  fopab2 2891  rnoprab 3033  xpassen 3344  sbthlem6 3354  unfilem1 3438  ac6lem 3575  pjrn 5587

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6  ax-4 673  ax-5 674  ax-6 675  ax-7 676  ax-gen 677  ax-8 798  ax-9 799  ax-10 800  ax-11 801  ax-12 802  ax-13 804  ax-14 805  ax-16 922  ax-17 925  ax-ext 1074  ax-rep 1075  ax-pow 1077

This theorem depends on definitions:  df-bi 128  df-or 197  df-an 198  df-ex 679  df-sb 853  df-clab 1093  df-cleq 1097  df-clel 1099  df-v 1349  df-dif 1489  df-un 1490  df-in 1491  df-ss 1492  df-nul 1708  df-pw 1799  df-sn 1811  df-pr 1812  df-op 1815  df-br 2063  df-opab 2098  df-cnv 2426  df-dm 2428  df-rn 2429

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