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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 1616 | . 2 |
3 | cbval2.3 | . . 3 | |
4 | 3 | nfex 1616 | . 2 |
5 | nfv 1508 | . . . . . 6 | |
6 | cbval2.2 | . . . . . 6 | |
7 | 5, 6 | nfan 1544 | . . . . 5 |
8 | nfv 1508 | . . . . . 6 | |
9 | cbval2.4 | . . . . . 6 | |
10 | 8, 9 | nfan 1544 | . . . . 5 |
11 | cbval2.5 | . . . . . . 7 | |
12 | 11 | expcom 115 | . . . . . 6 |
13 | 12 | pm5.32d 445 | . . . . 5 |
14 | 7, 10, 13 | cbvex 1729 | . . . 4 |
15 | 19.42v 1878 | . . . 4 | |
16 | 19.42v 1878 | . . . 4 | |
17 | 14, 15, 16 | 3bitr3i 209 | . . 3 |
18 | pm5.32 448 | . . 3 | |
19 | 17, 18 | mpbir 145 | . 2 |
20 | 2, 4, 19 | cbvex 1729 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wnf 1436 wex 1468 |
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-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 |
This theorem depends on definitions: df-bi 116 df-nf 1437 |
This theorem is referenced by: cbvex2v 1896 cbvopab 3999 cbvoprab12 5845 |
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