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Mirrors > Home > MPE Home > Th. List > Mathboxes > rncnv | Structured version Visualization version GIF version |
Description: Range of converse is the domain. (Contributed by Peter Mazsa, 12-Feb-2018.) |
Ref | Expression |
---|---|
rncnv | ⊢ ran ◡𝐴 = dom 𝐴 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dfdm4 5850 | . 2 ⊢ dom 𝐴 = ran ◡𝐴 | |
2 | 1 | eqcomi 2745 | 1 ⊢ ran ◡𝐴 = dom 𝐴 |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1541 ◡ccnv 5631 dom cdm 5632 ran crn 5633 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1797 ax-4 1811 ax-5 1913 ax-6 1971 ax-7 2011 ax-8 2108 ax-9 2116 ax-ext 2707 ax-sep 5255 ax-nul 5262 ax-pr 5383 |
This theorem depends on definitions: df-bi 206 df-an 397 df-or 846 df-3an 1089 df-tru 1544 df-fal 1554 df-ex 1782 df-sb 2068 df-clab 2714 df-cleq 2728 df-clel 2814 df-rab 3407 df-v 3446 df-dif 3912 df-un 3914 df-in 3916 df-ss 3926 df-nul 4282 df-if 4486 df-sn 4586 df-pr 4588 df-op 4592 df-br 5105 df-opab 5167 df-cnv 5640 df-dm 5642 df-rn 5643 |
This theorem is referenced by: dmcoss3 36904 symrelim 37010 symrefref2 37014 |
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