Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > cbvexv1 | Unicode version |
Description: Rule used to change bound variables, using implicit substitution. Version of cbvex 1736 with a disjoint variable condition. See cbvexvw 1900 for a version with two disjoint variable conditions, and cbvexv 1898 for another variant. (Contributed by NM, 21-Jun-1993.) (Revised by BJ, 31-May-2019.) |
Ref | Expression |
---|---|
cbvalv1.nf1 | |
cbvalv1.nf2 | |
cbvalv1.1 |
Ref | Expression |
---|---|
cbvexv1 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cbvalv1.nf2 | . . . 4 | |
2 | 1 | nfex 1617 | . . 3 |
3 | cbvalv1.nf1 | . . . . . 6 | |
4 | 3 | nfri 1499 | . . . . 5 |
5 | cbvalv1.1 | . . . . . . 7 | |
6 | 5 | bicomd 140 | . . . . . 6 |
7 | 6 | equcoms 1688 | . . . . 5 |
8 | 4, 7 | equsex 1708 | . . . 4 |
9 | exsimpr 1598 | . . . 4 | |
10 | 8, 9 | sylbir 134 | . . 3 |
11 | 2, 10 | exlimi 1574 | . 2 |
12 | 3 | nfex 1617 | . . 3 |
13 | 1 | nfri 1499 | . . . . 5 |
14 | 13, 5 | equsex 1708 | . . . 4 |
15 | exsimpr 1598 | . . . 4 | |
16 | 14, 15 | sylbir 134 | . . 3 |
17 | 12, 16 | exlimi 1574 | . 2 |
18 | 11, 17 | impbii 125 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wnf 1440 wex 1472 |
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 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 |
This theorem depends on definitions: df-bi 116 df-nf 1441 |
This theorem is referenced by: fprod2dlemstep 11512 |
Copyright terms: Public domain | W3C validator |