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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 |
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raleqbii.2 |
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Ref | Expression |
---|---|
rexeqbii |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | raleqbii.1 |
. . . 4
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2 | 1 | eleq2i 2254 |
. . 3
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3 | raleqbii.2 |
. . 3
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4 | 2, 3 | anbi12i 460 |
. 2
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5 | 4 | rexbii2 2498 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-5 1457 ax-gen 1459 ax-ie1 1503 ax-ie2 1504 ax-4 1520 ax-17 1536 ax-ial 1544 ax-ext 2169 |
This theorem depends on definitions: df-bi 117 df-cleq 2180 df-clel 2183 df-rex 2471 |
This theorem is referenced by: exmidsbthrlem 15011 |
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