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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 2090 | . . . . 5 | |
3 | 2 | anbi1d 452 | . . . 4 |
4 | 3 | exbidv 1746 | . . 3 |
5 | 2 | imbi1d 229 | . . . 4 |
6 | 5 | albidv 1745 | . . 3 |
7 | sb56 1806 | . . 3 | |
8 | 1, 4, 6, 7 | vtoclb 2656 | . 2 |
9 | 8 | bicomi 130 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 102 wb 103 wal 1282 wceq 1284 wex 1421 wcel 1433 cvv 2601 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-5 1376 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-11 1437 ax-4 1440 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-ext 2063 |
This theorem depends on definitions: df-bi 115 df-nf 1390 df-sb 1686 df-clab 2068 df-cleq 2074 df-clel 2077 df-v 2603 |
This theorem is referenced by: ceqex 2722 |
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