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Mirrors > Home > MPE Home > Th. List > isfildlem | Structured version Visualization version Unicode version |
Description: Lemma for isfild 21662. (Contributed by Mario Carneiro, 1-Dec-2013.) |
Ref | Expression |
---|---|
isfild.1 | |
isfild.2 |
Ref | Expression |
---|---|
isfildlem |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elex 3212 | . . 3 | |
2 | 1 | a1i 11 | . 2 |
3 | isfild.2 | . . . 4 | |
4 | ssexg 4804 | . . . . 5 | |
5 | 4 | expcom 451 | . . . 4 |
6 | 3, 5 | syl 17 | . . 3 |
7 | 6 | adantrd 484 | . 2 |
8 | eleq1 2689 | . . . . . 6 | |
9 | sseq1 3626 | . . . . . . 7 | |
10 | dfsbcq 3437 | . . . . . . 7 | |
11 | 9, 10 | anbi12d 747 | . . . . . 6 |
12 | 8, 11 | bibi12d 335 | . . . . 5 |
13 | 12 | imbi2d 330 | . . . 4 |
14 | nfv 1843 | . . . . . 6 | |
15 | nfv 1843 | . . . . . . 7 | |
16 | nfv 1843 | . . . . . . . 8 | |
17 | nfsbc1v 3455 | . . . . . . . 8 | |
18 | 16, 17 | nfan 1828 | . . . . . . 7 |
19 | 15, 18 | nfbi 1833 | . . . . . 6 |
20 | 14, 19 | nfim 1825 | . . . . 5 |
21 | eleq1 2689 | . . . . . . 7 | |
22 | sseq1 3626 | . . . . . . . 8 | |
23 | sbceq1a 3446 | . . . . . . . 8 | |
24 | 22, 23 | anbi12d 747 | . . . . . . 7 |
25 | 21, 24 | bibi12d 335 | . . . . . 6 |
26 | 25 | imbi2d 330 | . . . . 5 |
27 | isfild.1 | . . . . 5 | |
28 | 20, 26, 27 | chvar 2262 | . . . 4 |
29 | 13, 28 | vtoclg 3266 | . . 3 |
30 | 29 | com12 32 | . 2 |
31 | 2, 7, 30 | pm5.21ndd 369 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 196 wa 384 wceq 1483 wcel 1990 cvv 3200 wsbc 3435 wss 3574 |
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 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-v 3202 df-sbc 3436 df-in 3581 df-ss 3588 |
This theorem is referenced by: isfild 21662 |
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