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Mirrors > Home > MPE Home > Th. List > eltskm | Structured version Visualization version Unicode version |
Description: Belonging to . (Contributed by FL, 17-Apr-2011.) (Proof shortened by Mario Carneiro, 21-Sep-2014.) |
Ref | Expression |
---|---|
eltskm |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | tskmval 9661 | . . 3 | |
2 | 1 | eleq2d 2687 | . 2 |
3 | elex 3212 | . . . 4 | |
4 | 3 | a1i 11 | . . 3 |
5 | tskmid 9662 | . . . . 5 | |
6 | tskmcl 9663 | . . . . . 6 | |
7 | eleq2 2690 | . . . . . . . 8 | |
8 | eleq2 2690 | . . . . . . . 8 | |
9 | 7, 8 | imbi12d 334 | . . . . . . 7 |
10 | 9 | rspcv 3305 | . . . . . 6 |
11 | 6, 10 | ax-mp 5 | . . . . 5 |
12 | 5, 11 | syl5com 31 | . . . 4 |
13 | elex 3212 | . . . 4 | |
14 | 12, 13 | syl6 35 | . . 3 |
15 | elintrabg 4489 | . . . 4 | |
16 | 15 | a1i 11 | . . 3 |
17 | 4, 14, 16 | pm5.21ndd 369 | . 2 |
18 | 2, 17 | bitrd 268 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 196 wceq 1483 wcel 1990 wral 2912 crab 2916 cvv 3200 cint 4475 cfv 5888 ctsk 9570 ctskm 9659 |
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-groth 9645 |
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-int 4476 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-f1 5893 df-fo 5894 df-f1o 5895 df-fv 5896 df-er 7742 df-en 7956 df-dom 7957 df-tsk 9571 df-tskm 9660 |
This theorem is referenced by: (None) |
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