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 109 | . . . . 5 | |
2 | cbvraldva2.2 | . . . . 5 | |
3 | 1, 2 | eleq12d 2235 | . . . 4 |
4 | cbvraldva2.1 | . . . 4 | |
5 | 3, 4 | imbi12d 233 | . . 3 |
6 | 5 | cbvaldva 1915 | . 2 |
7 | df-ral 2447 | . 2 | |
8 | df-ral 2447 | . 2 | |
9 | 6, 7, 8 | 3bitr4g 222 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wal 1340 wceq 1342 wcel 2135 wral 2442 |
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 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-i5r 1522 ax-ext 2146 |
This theorem depends on definitions: df-bi 116 df-nf 1448 df-cleq 2157 df-clel 2160 df-ral 2447 |
This theorem is referenced by: cbvraldva 2698 acexmid 5835 tfrlem3ag 6268 tfrlem3a 6269 tfrlemi1 6291 tfr1onlem3ag 6296 |
Copyright terms: Public domain | W3C validator |