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Mirrors > Home > ILE Home > Th. List > sbbi | Unicode version |
Description: Equivalence inside and outside of a substitution are equivalent. (Contributed by NM, 5-Aug-1993.) |
Ref | Expression |
---|---|
sbbi |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dfbi2 385 | . . 3 | |
2 | 1 | sbbii 1738 | . 2 |
3 | sbim 1924 | . . . 4 | |
4 | sbim 1924 | . . . 4 | |
5 | 3, 4 | anbi12i 455 | . . 3 |
6 | sban 1926 | . . 3 | |
7 | dfbi2 385 | . . 3 | |
8 | 5, 6, 7 | 3bitr4i 211 | . 2 |
9 | 2, 8 | bitri 183 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 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-nf 1437 df-sb 1736 |
This theorem is referenced by: sblbis 1931 sbrbis 1932 sbco 1939 sbcocom 1941 elsb3 1949 elsb4 1950 sb8eu 2010 sb8euh 2020 pm13.183 2817 sbcbig 2950 sb8iota 5090 |
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