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Mirrors > Home > ILE Home > Th. List > sbcie2g | Unicode version |
Description: Conversion of implicit substitution to explicit class substitution. This version of sbcie 2797 avoids a disjointness condition on and by substituting twice. (Contributed by Mario Carneiro, 15-Oct-2016.) |
Ref | Expression |
---|---|
sbcie2g.1 | |
sbcie2g.2 |
Ref | Expression |
---|---|
sbcie2g |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dfsbcq 2766 | . 2 | |
2 | sbcie2g.2 | . 2 | |
3 | sbsbc 2768 | . . 3 | |
4 | nfv 1421 | . . . 4 | |
5 | sbcie2g.1 | . . . 4 | |
6 | 4, 5 | sbie 1674 | . . 3 |
7 | 3, 6 | bitr3i 175 | . 2 |
8 | 1, 2, 7 | vtoclbg 2614 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 98 wceq 1243 wcel 1393 wsb 1645 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-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: sbcel2gv 2822 csbie2g 2896 brab1 3809 |
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