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Mirrors > Home > ILE Home > Th. List > alexeq | Unicode version |
Description: Two ways to express substitution of for in . (Contributed by NM, 2-Mar-1995.) |
Ref | Expression |
---|---|
alexeq.1 |
Ref | Expression |
---|---|
alexeq |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | alexeq.1 | . . 3 | |
2 | eqeq2 2049 | . . . . 5 | |
3 | 2 | anbi1d 438 | . . . 4 |
4 | 3 | exbidv 1706 | . . 3 |
5 | 2 | imbi1d 220 | . . . 4 |
6 | 5 | albidv 1705 | . . 3 |
7 | sb56 1765 | . . 3 | |
8 | 1, 4, 6, 7 | vtoclb 2611 | . 2 |
9 | 8 | bicomi 123 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 97 wb 98 wal 1241 wceq 1243 wex 1381 wcel 1393 cvv 2557 |
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-5 1336 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-11 1397 ax-4 1400 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-ext 2022 |
This theorem depends on definitions: df-bi 110 df-nf 1350 df-sb 1646 df-clab 2027 df-cleq 2033 df-clel 2036 df-v 2559 |
This theorem is referenced by: ceqex 2671 |
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