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Mirrors > Home > ILE Home > Th. List > cbvsbc | Unicode version |
Description: Change bound variables in a wff substitution. (Contributed by Jeff Hankins, 19-Sep-2009.) (Proof shortened by Andrew Salmon, 8-Jun-2011.) |
Ref | Expression |
---|---|
cbvsbc.1 |
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cbvsbc.2 |
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cbvsbc.3 |
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Ref | Expression |
---|---|
cbvsbc |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cbvsbc.1 |
. . . 4
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2 | cbvsbc.2 |
. . . 4
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3 | cbvsbc.3 |
. . . 4
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4 | 1, 2, 3 | cbvab 2264 |
. . 3
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5 | 4 | eleq2i 2207 |
. 2
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6 | df-sbc 2914 |
. 2
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7 | df-sbc 2914 |
. 2
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8 | 5, 6, 7 | 3bitr4i 211 |
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-io 699 ax-5 1424 ax-7 1425 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1483 ax-10 1484 ax-11 1485 ax-i12 1486 ax-bndl 1487 ax-4 1488 ax-17 1507 ax-i9 1511 ax-ial 1515 ax-i5r 1516 ax-ext 2122 |
This theorem depends on definitions: df-bi 116 df-nf 1438 df-sb 1737 df-clab 2127 df-cleq 2133 df-clel 2136 df-sbc 2914 |
This theorem is referenced by: cbvsbcv 2942 cbvcsb 3012 |
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