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Mirrors > Home > ILE Home > Th. List > cbvral2vw | Unicode version |
Description: Change bound variables of double restricted universal quantification, using implicit substitution. Version of cbvral2v 2716 with a disjoint variable condition, which does not require ax-13 2150. (Contributed by NM, 10-Aug-2004.) (Revised by Gino Giotto, 10-Jan-2024.) |
Ref | Expression |
---|---|
cbvral2vw.1 |
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cbvral2vw.2 |
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Ref | Expression |
---|---|
cbvral2vw |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cbvral2vw.1 |
. . . 4
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2 | 1 | ralbidv 2477 |
. . 3
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3 | 2 | cbvralvw 2707 |
. 2
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4 | cbvral2vw.2 |
. . . 4
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5 | 4 | cbvralvw 2707 |
. . 3
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6 | 5 | ralbii 2483 |
. 2
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7 | 3, 6 | bitri 184 |
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 1447 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 |
This theorem depends on definitions: df-bi 117 df-tru 1356 df-nf 1461 df-clel 2173 df-ral 2460 |
This theorem is referenced by: mhmpropd 12747 |
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