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Mirrors > Home > ILE Home > Th. List > sb3an | Unicode version |
Description: Conjunction inside and outside of a substitution are equivalent. (Contributed by NM, 14-Dec-2006.) |
Ref | Expression |
---|---|
sb3an |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-3an 887 | . . 3 | |
2 | 1 | sbbii 1648 | . 2 |
3 | sban 1829 | . 2 | |
4 | sban 1829 | . . . 4 | |
5 | 4 | anbi1i 431 | . . 3 |
6 | df-3an 887 | . . 3 | |
7 | 5, 6 | bitr4i 176 | . 2 |
8 | 2, 3, 7 | 3bitri 195 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 97 wb 98 w3a 885 wsb 1645 |
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-4 1400 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 |
This theorem depends on definitions: df-bi 110 df-3an 887 df-nf 1350 df-sb 1646 |
This theorem is referenced by: sbc3ang 2820 |
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