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Mirrors > Home > ILE Home > Th. List > cbvex2 | Unicode version |
Description: Rule used to change bound variables, using implicit substitution. (Contributed by NM, 14-Sep-2003.) (Revised by Mario Carneiro, 6-Oct-2016.) |
Ref | Expression |
---|---|
cbval2.1 | |
cbval2.2 | |
cbval2.3 | |
cbval2.4 | |
cbval2.5 |
Ref | Expression |
---|---|
cbvex2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cbval2.1 | . . 3 | |
2 | 1 | nfex 1635 | . 2 |
3 | cbval2.3 | . . 3 | |
4 | 3 | nfex 1635 | . 2 |
5 | nfv 1526 | . . . . . 6 | |
6 | cbval2.2 | . . . . . 6 | |
7 | 5, 6 | nfan 1563 | . . . . 5 |
8 | nfv 1526 | . . . . . 6 | |
9 | cbval2.4 | . . . . . 6 | |
10 | 8, 9 | nfan 1563 | . . . . 5 |
11 | cbval2.5 | . . . . . . 7 | |
12 | 11 | expcom 116 | . . . . . 6 |
13 | 12 | pm5.32d 450 | . . . . 5 |
14 | 7, 10, 13 | cbvex 1754 | . . . 4 |
15 | 19.42v 1904 | . . . 4 | |
16 | 19.42v 1904 | . . . 4 | |
17 | 14, 15, 16 | 3bitr3i 210 | . . 3 |
18 | pm5.32 453 | . . 3 | |
19 | 17, 18 | mpbir 146 | . 2 |
20 | 2, 4, 19 | cbvex 1754 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 104 wb 105 wnf 1458 wex 1490 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-5 1445 ax-7 1446 ax-gen 1447 ax-ie1 1491 ax-ie2 1492 ax-8 1502 ax-4 1508 ax-17 1524 ax-i9 1528 ax-ial 1532 |
This theorem depends on definitions: df-bi 117 df-nf 1459 |
This theorem is referenced by: cbvex2v 1922 cbvopab 4069 cbvoprab12 5939 |
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