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Mirrors > Home > ILE Home > Th. List > sbc2iegf | Unicode version |
Description: Conversion of implicit substitution to explicit class substitution. (Contributed by Mario Carneiro, 19-Dec-2013.) |
Ref | Expression |
---|---|
sbc2iegf.1 | |
sbc2iegf.2 | |
sbc2iegf.3 | |
sbc2iegf.4 |
Ref | Expression |
---|---|
sbc2iegf |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | simpl 107 | . 2 | |
2 | simpl 107 | . . . 4 | |
3 | sbc2iegf.4 | . . . . 5 | |
4 | 3 | adantll 459 | . . . 4 |
5 | nfv 1461 | . . . 4 | |
6 | sbc2iegf.2 | . . . . 5 | |
7 | 6 | a1i 9 | . . . 4 |
8 | 2, 4, 5, 7 | sbciedf 2849 | . . 3 |
9 | 8 | adantll 459 | . 2 |
10 | nfv 1461 | . . 3 | |
11 | sbc2iegf.3 | . . 3 | |
12 | 10, 11 | nfan 1497 | . 2 |
13 | sbc2iegf.1 | . . 3 | |
14 | 13 | a1i 9 | . 2 |
15 | 1, 9, 12, 14 | sbciedf 2849 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 102 wb 103 wceq 1284 wnf 1389 wcel 1433 wsbc 2815 |
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-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-3an 921 df-tru 1287 df-nf 1390 df-sb 1686 df-clab 2068 df-cleq 2074 df-clel 2077 df-nfc 2208 df-v 2603 df-sbc 2816 |
This theorem is referenced by: sbc2ie 2885 opelopabaf 4028 |
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