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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 964 | . . 3 | |
2 | 1 | sbbii 1738 | . 2 |
3 | sban 1926 | . 2 | |
4 | sban 1926 | . . . 4 | |
5 | 4 | anbi1i 453 | . . 3 |
6 | df-3an 964 | . . 3 | |
7 | 5, 6 | bitr4i 186 | . 2 |
8 | 2, 3, 7 | 3bitri 205 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 103 wb 104 w3a 962 wsb 1735 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-nf 1437 df-sb 1736 |
This theorem is referenced by: (None) |
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