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Mirrors > Home > ILE Home > Th. List > rexeqbii | Unicode version |
Description: Equality deduction for restricted existential quantifier, changing both formula and quantifier domain. Inference form. (Contributed by David Moews, 1-May-2017.) |
Ref | Expression |
---|---|
raleqbii.1 | |
raleqbii.2 |
Ref | Expression |
---|---|
rexeqbii |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | raleqbii.1 | . . . 4 | |
2 | 1 | eleq2i 2104 | . . 3 |
3 | raleqbii.2 | . . 3 | |
4 | 2, 3 | anbi12i 433 | . 2 |
5 | 4 | rexbii2 2335 | 1 |
Colors of variables: wff set class |
Syntax hints: wb 98 wceq 1243 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-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-4 1400 ax-17 1419 ax-ial 1427 ax-ext 2022 |
This theorem depends on definitions: df-bi 110 df-cleq 2033 df-clel 2036 df-rex 2312 |
This theorem is referenced by: (None) |
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