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Mirrors > Home > ILE Home > Th. List > cbvexh | Unicode version |
Description: Rule used to change bound variables, using implicit substitition. (Contributed by NM, 5-Aug-1993.) (Revised by Mario Carneiro, 3-Feb-2015.) |
Ref | Expression |
---|---|
cbvexh.1 | |
cbvexh.2 | |
cbvexh.3 |
Ref | Expression |
---|---|
cbvexh |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cbvexh.2 | . . . 4 | |
2 | 1 | hbex 1600 | . . 3 |
3 | cbvexh.1 | . . . . 5 | |
4 | cbvexh.3 | . . . . . . 7 | |
5 | 4 | bicomd 140 | . . . . . 6 |
6 | 5 | equcoms 1669 | . . . . 5 |
7 | 3, 6 | equsex 1691 | . . . 4 |
8 | simpr 109 | . . . . 5 | |
9 | 8 | eximi 1564 | . . . 4 |
10 | 7, 9 | sylbir 134 | . . 3 |
11 | 2, 10 | exlimih 1557 | . 2 |
12 | 3 | hbex 1600 | . . 3 |
13 | 1, 4 | equsex 1691 | . . . 4 |
14 | simpr 109 | . . . . 5 | |
15 | 14 | eximi 1564 | . . . 4 |
16 | 13, 15 | sylbir 134 | . . 3 |
17 | 12, 16 | exlimih 1557 | . 2 |
18 | 11, 17 | impbii 125 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wal 1314 wceq 1316 wex 1453 |
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 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-4 1472 ax-17 1491 ax-i9 1495 ax-ial 1499 |
This theorem depends on definitions: df-bi 116 |
This theorem is referenced by: cbvex 1714 sb8eh 1811 cbvexv 1872 euf 1982 mopick 2055 |
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