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Mirrors > Home > MPE Home > Th. List > sbnfc2 | Unicode version |
Description: Two ways of expressing " is (effectively) not free in ." (Contributed by Mario Carneiro, 14-Oct-2016.) |
Ref | Expression |
---|---|
sbnfc2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | vex 3112 | . . . . 5 | |
2 | csbtt 3445 | . . . . 5 | |
3 | 1, 2 | mpan 670 | . . . 4 |
4 | vex 3112 | . . . . 5 | |
5 | csbtt 3445 | . . . . 5 | |
6 | 4, 5 | mpan 670 | . . . 4 |
7 | 3, 6 | eqtr4d 2501 | . . 3 |
8 | 7 | alrimivv 1720 | . 2 |
9 | nfv 1707 | . . 3 | |
10 | eleq2 2530 | . . . . . 6 | |
11 | sbsbc 3331 | . . . . . . 7 | |
12 | sbcel2 3831 | . . . . . . 7 | |
13 | 11, 12 | bitri 249 | . . . . . 6 |
14 | sbsbc 3331 | . . . . . . 7 | |
15 | sbcel2 3831 | . . . . . . 7 | |
16 | 14, 15 | bitri 249 | . . . . . 6 |
17 | 10, 13, 16 | 3bitr4g 288 | . . . . 5 |
18 | 17 | 2alimi 1634 | . . . 4 |
19 | sbnf2 2183 | . . . 4 | |
20 | 18, 19 | sylibr 212 | . . 3 |
21 | 9, 20 | nfcd 2613 | . 2 |
22 | 8, 21 | impbii 188 | 1 |
Colors of variables: wff setvar class |
Syntax hints: <-> wb 184 A. wal 1393
= wceq 1395 F/ wnf 1616 [ wsb 1739
e. wcel 1818 F/_ wnfc 2605 cvv 3109
[. wsbc 3327 [_ csb 3434 |
This theorem is referenced by: eusvnf 4647 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1618 ax-4 1631 ax-5 1704 ax-6 1747 ax-7 1790 ax-10 1837 ax-11 1842 ax-12 1854 ax-13 1999 ax-ext 2435 |
This theorem depends on definitions: df-bi 185 df-or 370 df-an 371 df-tru 1398 df-fal 1401 df-ex 1613 df-nf 1617 df-sb 1740 df-clab 2443 df-cleq 2449 df-clel 2452 df-nfc 2607 df-v 3111 df-sbc 3328 df-csb 3435 df-dif 3478 df-in 3482 df-ss 3489 df-nul 3785 |
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