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Mirrors > Home > MPE Home > Th. List > rnxp | Structured version Visualization version Unicode version |
Description: The range of a Cartesian product. Part of Theorem 3.13(x) of [Monk1] p. 37. (Contributed by NM, 12-Apr-2004.) |
Ref | Expression |
---|---|
rnxp |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-rn 5125 | . . 3 | |
2 | cnvxp 5551 | . . . 4 | |
3 | 2 | dmeqi 5325 | . . 3 |
4 | 1, 3 | eqtri 2644 | . 2 |
5 | dmxp 5344 | . 2 | |
6 | 4, 5 | syl5eq 2668 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wceq 1483 wne 2794 c0 3915 cxp 5112 ccnv 5113 cdm 5114 crn 5115 |
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-ne 2795 df-ral 2917 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-rel 5121 df-cnv 5122 df-dm 5124 df-rn 5125 |
This theorem is referenced by: rnxpid 5567 ssxpb 5568 xpima 5576 unixp 5668 fconst5 6471 xpexr 7106 xpexr2 7107 fparlem3 7279 fparlem4 7280 frxp 7287 fodomr 8111 dfac5lem3 8948 fpwwe2lem13 9464 vdwlem8 15692 ramz 15729 gsumxp 18375 xkoccn 21422 txindislem 21436 cnextf 21870 metustexhalf 22361 ovolctb 23258 axlowdimlem13 25834 axlowdim1 25839 imadifxp 29414 sibf0 30396 ovoliunnfl 33451 voliunnfl 33453 |
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