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Mirrors > Home > ILE Home > Th. List > sbcan | Unicode version |
Description: Distribution of class substitution over conjunction. (Contributed by NM, 31-Dec-2016.) |
Ref | Expression |
---|---|
sbcan |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sbcex 2772 | . 2 | |
2 | sbcex 2772 | . . 3 | |
3 | 2 | adantl 262 | . 2 |
4 | dfsbcq2 2767 | . . 3 | |
5 | dfsbcq2 2767 | . . . 4 | |
6 | dfsbcq2 2767 | . . . 4 | |
7 | 5, 6 | anbi12d 442 | . . 3 |
8 | sban 1829 | . . 3 | |
9 | 4, 7, 8 | vtoclbg 2614 | . 2 |
10 | 1, 3, 9 | pm5.21nii 620 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 97 wb 98 wceq 1243 wcel 1393 wsb 1645 cvv 2557 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: difopab 4469 sbcfung 4925 sbcfng 5044 sbcfg 5045 |
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