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Mirrors > Home > MPE Home > Th. List > Mathboxes > riotasv3d | Structured version Visualization version Unicode version |
Description: A property holding for a representative of a single-valued class expression (see e.g. reusv2 4874) also holds for its description binder (in the form of property ). (Contributed by NM, 5-Mar-2013.) (Revised by Mario Carneiro, 15-Oct-2016.) |
Ref | Expression |
---|---|
riotasv3d.1 | |
riotasv3d.2 | |
riotasv3d.3 | |
riotasv3d.4 | |
riotasv3d.5 | |
riotasv3d.6 | |
riotasv3d.7 |
Ref | Expression |
---|---|
riotasv3d |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elex 3212 | . 2 | |
2 | riotasv3d.7 | . . . 4 | |
3 | 2 | adantr 481 | . . 3 |
4 | riotasv3d.1 | . . . . . 6 | |
5 | nfv 1843 | . . . . . 6 | |
6 | riotasv3d.5 | . . . . . . . . . 10 | |
7 | 6 | imp 445 | . . . . . . . . 9 |
8 | 7 | adantrl 752 | . . . . . . . 8 |
9 | riotasv3d.3 | . . . . . . . . . . . 12 | |
10 | riotasv3d.6 | . . . . . . . . . . . 12 | |
11 | 9, 10 | riotasvd 34242 | . . . . . . . . . . 11 |
12 | 11 | impr 649 | . . . . . . . . . 10 |
13 | 12 | eqcomd 2628 | . . . . . . . . 9 |
14 | riotasv3d.4 | . . . . . . . . 9 | |
15 | 13, 14 | syldan 487 | . . . . . . . 8 |
16 | 8, 15 | mpbid 222 | . . . . . . 7 |
17 | 16 | exp45 642 | . . . . . 6 |
18 | 4, 5, 17 | ralrimd 2959 | . . . . 5 |
19 | riotasv3d.2 | . . . . . 6 | |
20 | r19.23t 3021 | . . . . . 6 | |
21 | 19, 20 | syl 17 | . . . . 5 |
22 | 18, 21 | sylibd 229 | . . . 4 |
23 | 22 | imp 445 | . . 3 |
24 | 3, 23 | mpd 15 | . 2 |
25 | 1, 24 | sylan2 491 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 196 wa 384 wceq 1483 wnf 1708 wcel 1990 wral 2912 wrex 2913 cvv 3200 crio 6610 |
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 ax-riotaBAD 34239 |
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-nel 2898 df-ral 2917 df-rex 2918 df-reu 2919 df-rab 2921 df-v 3202 df-sbc 3436 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-iota 5851 df-fun 5890 df-fv 5896 df-riota 6611 df-undef 7399 |
This theorem is referenced by: cdlemefs32sn1aw 35702 cdleme43fsv1snlem 35708 cdleme41sn3a 35721 cdleme40m 35755 cdleme40n 35756 cdlemkid 36224 dihvalcqpre 36524 |
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