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Mirrors > Home > MPE Home > Th. List > rnxpss | Structured version Visualization version Unicode version |
Description: The range of a Cartesian product is a subclass of the second factor. (Contributed by NM, 16-Jan-2006.) (Proof shortened by Andrew Salmon, 27-Aug-2011.) |
Ref | Expression |
---|---|
rnxpss |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-rn 5125 | . 2 | |
2 | cnvxp 5551 | . . . 4 | |
3 | 2 | dmeqi 5325 | . . 3 |
4 | dmxpss 5565 | . . 3 | |
5 | 3, 4 | eqsstri 3635 | . 2 |
6 | 1, 5 | eqsstri 3635 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wss 3574 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: ssxpb 5568 ssrnres 5572 funssxp 6061 fconst 6091 dff2 6371 dff3 6372 fliftf 6565 marypha1lem 8339 marypha1 8340 dfac12lem2 8966 brdom4 9352 nqerf 9752 xptrrel 13719 lern 17225 cnconst2 21087 lmss 21102 tsmsxplem1 21956 causs 23096 i1f0 23454 itg10 23455 taylf 24115 perpln2 25606 locfinref 29908 sitg0 30408 noextendseq 31820 heicant 33444 rntrclfvOAI 37254 rtrclex 37924 trclexi 37927 rtrclexi 37928 cnvtrcl0 37933 rntrcl 37935 brtrclfv2 38019 rp-imass 38065 xphe 38075 rfovcnvf1od 38298 |
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