Theorem rncnv 38008

Description: Range of converse is the domain. (Contributed by Peter Mazsa, 12-Feb-2018.)

Assertion

Ref	Expression
rncnv	⊢ ran ◡𝐴 = dom 𝐴

Proof of Theorem rncnv

Step	Hyp	Ref	Expression
1		dfdm4 5892	. 2 ⊢ dom 𝐴 = ran ◡𝐴
2	1	eqcomi 2735	1 ⊢ ran ◡𝐴 = dom 𝐴

Syntax hints:   = wceq 1534  ^◡ccnv 5671  dom cdm 5672  ran crn 5673

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1790  ax-4 1804  ax-5 1906  ax-6 1964  ax-7 2004  ax-8 2101  ax-9 2109  ax-ext 2697  ax-sep 5294  ax-nul 5301  ax-pr 5423

This theorem depends on definitions:  df-bi 206  df-an 395  df-or 846  df-3an 1086  df-tru 1537  df-fal 1547  df-ex 1775  df-sb 2061  df-clab 2704  df-cleq 2718  df-clel 2803  df-rab 3420  df-v 3464  df-dif 3949  df-un 3951  df-ss 3963  df-nul 4323  df-if 4524  df-sn 4624  df-pr 4626  df-op 4630  df-br 5144  df-opab 5206  df-cnv 5680  df-dm 5682  df-rn 5683

This theorem is referenced by:  dmcoss3  38161  symrelim  38267  symrefref2  38271