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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 386 | . . 3 | |
2 | 1 | sbbii 1758 | . 2 |
3 | sbim 1946 | . . . 4 | |
4 | sbim 1946 | . . . 4 | |
5 | 3, 4 | anbi12i 457 | . . 3 |
6 | sban 1948 | . . 3 | |
7 | dfbi2 386 | . . 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 1755 |
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 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 |
This theorem depends on definitions: df-bi 116 df-nf 1454 df-sb 1756 |
This theorem is referenced by: sblbis 1953 sbrbis 1954 sbco 1961 sbcocom 1963 sb8eu 2032 sb8euh 2042 elsb1 2148 elsb2 2149 pm13.183 2868 sbcbig 3001 sb8iota 5165 |
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