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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 102 | . 2 | |
2 | simpl 102 | . . . 4 | |
3 | sbc2iegf.4 | . . . . 5 | |
4 | 3 | adantll 445 | . . . 4 |
5 | nfv 1421 | . . . 4 | |
6 | sbc2iegf.2 | . . . . 5 | |
7 | 6 | a1i 9 | . . . 4 |
8 | 2, 4, 5, 7 | sbciedf 2798 | . . 3 |
9 | 8 | adantll 445 | . 2 |
10 | nfv 1421 | . . 3 | |
11 | sbc2iegf.3 | . . 3 | |
12 | 10, 11 | nfan 1457 | . 2 |
13 | sbc2iegf.1 | . . 3 | |
14 | 13 | a1i 9 | . 2 |
15 | 1, 9, 12, 14 | sbciedf 2798 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 97 wb 98 wceq 1243 wnf 1349 wcel 1393 wsbc 2764 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-io 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-bndl 1399 ax-4 1400 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 |
This theorem depends on definitions: df-bi 110 df-3an 887 df-tru 1246 df-nf 1350 df-sb 1646 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-v 2559 df-sbc 2765 |
This theorem is referenced by: sbc2ie 2829 opelopabaf 4010 |
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