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Mirrors > Home > ILE Home > Th. List > cbvaldvaw | Unicode version |
Description: Rule used to change the bound variable in a universal quantifier with implicit substitution. Deduction form. Version of cbvaldva 1940 with a disjoint variable condition. (Contributed by David Moews, 1-May-2017.) (Revised by GG, 10-Jan-2024.) (Revised by Wolf Lammen, 10-Feb-2024.) |
Ref | Expression |
---|---|
cbvaldvaw.1 |
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Ref | Expression |
---|---|
cbvaldvaw |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cbvaldvaw.1 |
. . . . . 6
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2 | 1 | ancoms 268 |
. . . . 5
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3 | 2 | pm5.74da 443 |
. . . 4
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4 | 3 | cbvalvw 1931 |
. . 3
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5 | 19.21v 1884 |
. . 3
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6 | 19.21v 1884 |
. . 3
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7 | 4, 5, 6 | 3bitr3i 210 |
. 2
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8 | 7 | pm5.74ri 181 |
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 1458 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-i5r 1546 |
This theorem depends on definitions: df-bi 117 df-nf 1472 |
This theorem is referenced by: cbval2vw 1944 |
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