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Mirrors > Home > MPE Home > Th. List > isssp | Structured version Visualization version Unicode version |
Description: The predicate "is a subspace." (Contributed by NM, 26-Jan-2008.) (New usage is discouraged.) |
Ref | Expression |
---|---|
isssp.g | |
isssp.f | |
isssp.s | |
isssp.r | |
isssp.n | CV |
isssp.m | CV |
isssp.h |
Ref | Expression |
---|---|
isssp |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | isssp.g | . . . 4 | |
2 | isssp.s | . . . 4 | |
3 | isssp.n | . . . 4 CV | |
4 | isssp.h | . . . 4 | |
5 | 1, 2, 3, 4 | sspval 27578 | . . 3 CV |
6 | 5 | eleq2d 2687 | . 2 CV |
7 | fveq2 6191 | . . . . . 6 | |
8 | isssp.f | . . . . . 6 | |
9 | 7, 8 | syl6eqr 2674 | . . . . 5 |
10 | 9 | sseq1d 3632 | . . . 4 |
11 | fveq2 6191 | . . . . . 6 | |
12 | isssp.r | . . . . . 6 | |
13 | 11, 12 | syl6eqr 2674 | . . . . 5 |
14 | 13 | sseq1d 3632 | . . . 4 |
15 | fveq2 6191 | . . . . . 6 CV CV | |
16 | isssp.m | . . . . . 6 CV | |
17 | 15, 16 | syl6eqr 2674 | . . . . 5 CV |
18 | 17 | sseq1d 3632 | . . . 4 CV |
19 | 10, 14, 18 | 3anbi123d 1399 | . . 3 CV |
20 | 19 | elrab 3363 | . 2 CV |
21 | 6, 20 | syl6bb 276 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 196 wa 384 w3a 1037 wceq 1483 wcel 1990 crab 2916 wss 3574 cfv 5888 cnv 27439 cpv 27440 cns 27442 CVcnmcv 27445 css 27576 |
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-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-rn 5125 df-res 5126 df-ima 5127 df-iota 5851 df-fun 5890 df-fn 5891 df-f 5892 df-fo 5894 df-fv 5896 df-oprab 6654 df-1st 7168 df-2nd 7169 df-vc 27414 df-nv 27447 df-va 27450 df-sm 27452 df-nmcv 27455 df-ssp 27577 |
This theorem is referenced by: sspid 27580 sspnv 27581 sspba 27582 sspg 27583 ssps 27585 sspn 27591 hhsst 28123 hhsssh2 28127 |
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