Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > cbvraldva2 | Unicode version |
Description: Rule used to change the bound variable in a restricted universal quantifier with implicit substitution which also changes the quantifier domain. Deduction form. (Contributed by David Moews, 1-May-2017.) |
Ref | Expression |
---|---|
cbvraldva2.1 | |
cbvraldva2.2 |
Ref | Expression |
---|---|
cbvraldva2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | simpr 108 | . . . . 5 | |
2 | cbvraldva2.2 | . . . . 5 | |
3 | 1, 2 | eleq12d 2149 | . . . 4 |
4 | cbvraldva2.1 | . . . 4 | |
5 | 3, 4 | imbi12d 232 | . . 3 |
6 | 5 | cbvaldva 1844 | . 2 |
7 | df-ral 2353 | . 2 | |
8 | df-ral 2353 | . 2 | |
9 | 6, 7, 8 | 3bitr4g 221 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 102 wb 103 wal 1282 wceq 1284 wcel 1433 wral 2348 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-4 1440 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468 ax-ext 2063 |
This theorem depends on definitions: df-bi 115 df-nf 1390 df-cleq 2074 df-clel 2077 df-ral 2353 |
This theorem is referenced by: cbvraldva 2583 acexmid 5531 tfrlem3ag 5947 tfrlem3a 5948 tfrlemi1 5969 |
Copyright terms: Public domain | W3C validator |