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Mirrors > Home > ILE Home > Th. List > cbvrexdva2 | Unicode version |
Description: Rule used to change the bound variable in a restricted existential 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 |
---|---|
cbvrexdva2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | simpr 103 | . . . . 5 | |
2 | cbvraldva2.2 | . . . . 5 | |
3 | 1, 2 | eleq12d 2108 | . . . 4 |
4 | cbvraldva2.1 | . . . 4 | |
5 | 3, 4 | anbi12d 442 | . . 3 |
6 | 5 | cbvexdva 1804 | . 2 |
7 | df-rex 2312 | . 2 | |
8 | df-rex 2312 | . 2 | |
9 | 6, 7, 8 | 3bitr4g 212 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 97 wb 98 wceq 1243 wex 1381 wcel 1393 wrex 2307 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-4 1400 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-ext 2022 |
This theorem depends on definitions: df-bi 110 df-nf 1350 df-cleq 2033 df-clel 2036 df-rex 2312 |
This theorem is referenced by: cbvrexdva 2540 acexmid 5511 |
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