Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > sbcnel12g | Unicode version |
Description: Distribute proper substitution through negated membership. (Contributed by Andrew Salmon, 18-Jun-2011.) |
Ref | Expression |
---|---|
sbcnel12g |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-nel 2340 | . . . 4 | |
2 | 1 | sbcbii 2873 | . . 3 |
3 | 2 | a1i 9 | . 2 |
4 | sbcng 2854 | . 2 | |
5 | sbcel12g 2921 | . . . 4 | |
6 | 5 | notbid 624 | . . 3 |
7 | df-nel 2340 | . . 3 | |
8 | 6, 7 | syl6bbr 196 | . 2 |
9 | 3, 4, 8 | 3bitrd 212 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wb 103 wcel 1433 wnel 2339 wsbc 2815 csb 2908 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-in1 576 ax-in2 577 ax-io 662 ax-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-10 1436 ax-11 1437 ax-i12 1438 ax-bndl 1439 ax-4 1440 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468 ax-ext 2063 |
This theorem depends on definitions: df-bi 115 df-tru 1287 df-fal 1290 df-nf 1390 df-sb 1686 df-clab 2068 df-cleq 2074 df-clel 2077 df-nfc 2208 df-nel 2340 df-v 2603 df-sbc 2816 df-csb 2909 |
This theorem is referenced by: (None) |
Copyright terms: Public domain | W3C validator |