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Mirrors > Home > MPE Home > Th. List > cnvimarndm | Structured version Visualization version Unicode version |
Description: The preimage of the range of a class is the domain of the class. (Contributed by Jeff Hankins, 15-Jul-2009.) |
Ref | Expression |
---|---|
cnvimarndm |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | imadmrn 5476 | . 2 | |
2 | df-rn 5125 | . . 3 | |
3 | 2 | imaeq2i 5464 | . 2 |
4 | dfdm4 5316 | . 2 | |
5 | 1, 3, 4 | 3eqtr4i 2654 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wceq 1483 ccnv 5113 cdm 5114 crn 5115 cima 5117 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 ax-sep 4781 ax-nul 4789 ax-pr 4906 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-3an 1039 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-eu 2474 df-mo 2475 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-ral 2917 df-rex 2918 df-rab 2921 df-v 3202 df-dif 3577 df-un 3579 df-in 3581 df-ss 3588 df-nul 3916 df-if 4087 df-sn 4178 df-pr 4180 df-op 4184 df-br 4654 df-opab 4713 df-xp 5120 df-cnv 5122 df-dm 5124 df-rn 5125 df-res 5126 df-ima 5127 |
This theorem is referenced by: cnrest2 21090 mbfconstlem 23396 i1fima 23445 i1fima2 23446 i1fd 23448 i1f0rn 23449 itg1addlem5 23467 fcoinver 29418 sibfof 30402 itg2addnclem 33461 itg2addnclem2 33462 ftc1anclem6 33490 |
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