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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 2147 | . . . . 5 | |
3 | 2 | anbi1d 460 | . . . 4 |
4 | 3 | exbidv 1797 | . . 3 |
5 | 2 | imbi1d 230 | . . . 4 |
6 | 5 | albidv 1796 | . . 3 |
7 | sb56 1857 | . . 3 | |
8 | 1, 4, 6, 7 | vtoclb 2738 | . 2 |
9 | 8 | bicomi 131 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wal 1329 wceq 1331 wex 1468 wcel 1480 cvv 2681 |
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-5 1423 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-11 1484 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-ext 2119 |
This theorem depends on definitions: df-bi 116 df-nf 1437 df-sb 1736 df-clab 2124 df-cleq 2130 df-clel 2133 df-v 2683 |
This theorem is referenced by: ceqex 2807 |
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