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Mirrors > Home > ILE Home > Th. List > raleqbii | Unicode version |
Description: Equality deduction for restricted universal quantifier, changing both formula and quantifier domain. Inference form. (Contributed by David Moews, 1-May-2017.) |
Ref | Expression |
---|---|
raleqbii.1 | |
raleqbii.2 |
Ref | Expression |
---|---|
raleqbii |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | raleqbii.1 | . . . 4 | |
2 | 1 | eleq2i 2204 | . . 3 |
3 | raleqbii.2 | . . 3 | |
4 | 2, 3 | imbi12i 238 | . 2 |
5 | 4 | ralbii2 2443 | 1 |
Colors of variables: wff set class |
Syntax hints: wb 104 wceq 1331 wcel 1480 wral 2414 |
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-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-4 1487 ax-17 1506 ax-ial 1514 ax-ext 2119 |
This theorem depends on definitions: df-bi 116 df-cleq 2130 df-clel 2133 df-ral 2419 |
This theorem is referenced by: (None) |
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