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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 |
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cbvraldva2.2 |
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Ref | Expression |
---|---|
cbvrexdva2 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | simpr 109 |
. . . . 5
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2 | cbvraldva2.2 |
. . . . 5
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3 | 1, 2 | eleq12d 2211 |
. . . 4
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4 | cbvraldva2.1 |
. . . 4
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5 | 3, 4 | anbi12d 465 |
. . 3
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6 | 5 | cbvexdva 1902 |
. 2
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7 | df-rex 2423 |
. 2
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8 | df-rex 2423 |
. 2
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9 | 6, 7, 8 | 3bitr4g 222 |
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 105 ax-ia2 106 ax-ia3 107 ax-5 1424 ax-7 1425 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1483 ax-4 1488 ax-17 1507 ax-i9 1511 ax-ial 1515 ax-ext 2122 |
This theorem depends on definitions: df-bi 116 df-nf 1438 df-cleq 2133 df-clel 2136 df-rex 2423 |
This theorem is referenced by: cbvrexdva 2667 acexmid 5781 |
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