Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
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 2689 | . . . . 5 | |
2 | csbtt 3014 | . . . . 5 | |
3 | 1, 2 | mpan 420 | . . . 4 |
4 | vex 2689 | . . . . 5 | |
5 | csbtt 3014 | . . . . 5 | |
6 | 4, 5 | mpan 420 | . . . 4 |
7 | 3, 6 | eqtr4d 2175 | . . 3 |
8 | 7 | alrimivv 1847 | . 2 |
9 | nfv 1508 | . . 3 | |
10 | eleq2 2203 | . . . . . 6 | |
11 | sbsbc 2913 | . . . . . . 7 | |
12 | sbcel2g 3023 | . . . . . . . 8 | |
13 | 1, 12 | ax-mp 5 | . . . . . . 7 |
14 | 11, 13 | bitri 183 | . . . . . 6 |
15 | sbsbc 2913 | . . . . . . 7 | |
16 | sbcel2g 3023 | . . . . . . . 8 | |
17 | 4, 16 | ax-mp 5 | . . . . . . 7 |
18 | 15, 17 | bitri 183 | . . . . . 6 |
19 | 10, 14, 18 | 3bitr4g 222 | . . . . 5 |
20 | 19 | 2alimi 1432 | . . . 4 |
21 | sbnf2 1956 | . . . 4 | |
22 | 20, 21 | sylibr 133 | . . 3 |
23 | 9, 22 | nfcd 2276 | . 2 |
24 | 8, 23 | impbii 125 | 1 |
Colors of variables: wff set class |
Syntax hints: wb 104 wal 1329 wceq 1331 wnf 1436 wcel 1480 wsb 1735 wnfc 2268 cvv 2686 wsbc 2909 csb 3003 |
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 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2121 |
This theorem depends on definitions: df-bi 116 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-v 2688 df-sbc 2910 df-csb 3004 |
This theorem is referenced by: eusvnf 4374 |
Copyright terms: Public domain | W3C validator |