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Mirrors > Home > ILE 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 2663 | . . . . 5 | |
2 | csbtt 2985 | . . . . 5 | |
3 | 1, 2 | mpan 420 | . . . 4 |
4 | vex 2663 | . . . . 5 | |
5 | csbtt 2985 | . . . . 5 | |
6 | 4, 5 | mpan 420 | . . . 4 |
7 | 3, 6 | eqtr4d 2153 | . . 3 |
8 | 7 | alrimivv 1831 | . 2 |
9 | nfv 1493 | . . 3 | |
10 | eleq2 2181 | . . . . . 6 | |
11 | sbsbc 2886 | . . . . . . 7 | |
12 | sbcel2g 2994 | . . . . . . . 8 | |
13 | 1, 12 | ax-mp 5 | . . . . . . 7 |
14 | 11, 13 | bitri 183 | . . . . . 6 |
15 | sbsbc 2886 | . . . . . . 7 | |
16 | sbcel2g 2994 | . . . . . . . 8 | |
17 | 4, 16 | ax-mp 5 | . . . . . . 7 |
18 | 15, 17 | bitri 183 | . . . . . 6 |
19 | 10, 14, 18 | 3bitr4g 222 | . . . . 5 |
20 | 19 | 2alimi 1417 | . . . 4 |
21 | sbnf2 1934 | . . . 4 | |
22 | 20, 21 | sylibr 133 | . . 3 |
23 | 9, 22 | nfcd 2253 | . 2 |
24 | 8, 23 | impbii 125 | 1 |
Colors of variables: wff set class |
Syntax hints: wb 104 wal 1314 wceq 1316 wnf 1421 wcel 1465 wsb 1720 wnfc 2245 cvv 2660 wsbc 2882 csb 2975 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 683 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-10 1468 ax-11 1469 ax-i12 1470 ax-bndl 1471 ax-4 1472 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 |
This theorem depends on definitions: df-bi 116 df-tru 1319 df-nf 1422 df-sb 1721 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-v 2662 df-sbc 2883 df-csb 2976 |
This theorem is referenced by: eusvnf 4344 |
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