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Mirrors > Home > MPE Home > Th. List > ustssxp | Structured version Visualization version Unicode version |
Description: Entourages are subsets of the Cartesian product of the base set. (Contributed by Thierry Arnoux, 19-Nov-2017.) |
Ref | Expression |
---|---|
ustssxp | UnifOn |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elfvex 6221 | . . . . . 6 UnifOn | |
2 | isust 22007 | . . . . . 6 UnifOn | |
3 | 1, 2 | syl 17 | . . . . 5 UnifOn UnifOn |
4 | 3 | ibi 256 | . . . 4 UnifOn |
5 | 4 | simp1d 1073 | . . 3 UnifOn |
6 | 5 | sselda 3603 | . 2 UnifOn |
7 | 6 | elpwid 4170 | 1 UnifOn |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 196 wa 384 w3a 1037 wcel 1990 wral 2912 wrex 2913 cvv 3200 cin 3573 wss 3574 cpw 4158 cid 5023 cxp 5112 ccnv 5113 cres 5116 ccom 5118 cfv 5888 UnifOncust 22003 |
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-8 1992 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-pow 4843 ax-pr 4906 ax-un 6949 |
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-rex 2918 df-rab 2921 df-v 3202 df-sbc 3436 df-csb 3534 df-dif 3577 df-un 3579 df-in 3581 df-ss 3588 df-nul 3916 df-if 4087 df-pw 4160 df-sn 4178 df-pr 4180 df-op 4184 df-uni 4437 df-br 4654 df-opab 4713 df-mpt 4730 df-id 5024 df-xp 5120 df-rel 5121 df-cnv 5122 df-co 5123 df-dm 5124 df-res 5126 df-iota 5851 df-fun 5890 df-fv 5896 df-ust 22004 |
This theorem is referenced by: ustrel 22015 ustssco 22018 ustuni 22030 ustimasn 22032 trust 22033 utopbas 22039 ustuqtop1 22045 utop2nei 22054 utopreg 22056 ucnima 22085 ucnprima 22086 neipcfilu 22100 |
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