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Mirrors > Home > ILE Home > Th. List > cbvalh | Unicode version |
Description: Rule used to change bound variables, using implicit substitition. (Contributed by NM, 5-Aug-1993.) (Proof shortened by Andrew Salmon, 25-May-2011.) |
Ref | Expression |
---|---|
cbvalh.1 |
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cbvalh.2 |
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cbvalh.3 |
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Ref | Expression |
---|---|
cbvalh |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cbvalh.1 |
. . 3
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2 | cbvalh.2 |
. . 3
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3 | cbvalh.3 |
. . . 4
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4 | 3 | biimpd 143 |
. . 3
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5 | 1, 2, 4 | cbv3h 1722 |
. 2
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6 | 3 | equcoms 1685 |
. . . 4
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7 | 6 | biimprd 157 |
. . 3
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8 | 2, 1, 7 | cbv3h 1722 |
. 2
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9 | 5, 8 | impbii 125 |
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 |
This theorem depends on definitions: df-bi 116 df-nf 1438 |
This theorem is referenced by: cbval 1728 sb8h 1827 cbvalv 1890 sb9v 1954 sb8euh 2023 |
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