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Mirrors > Home > NFE Home > Th. List > cbvalw | Unicode version |
Description: Change bound variable. Uses only Tarski's FOL axiom schemes. (Contributed by NM, 9-Apr-2017.) |
Ref | Expression |
---|---|
cbvalw.1 |
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cbvalw.2 |
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cbvalw.3 |
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cbvalw.4 |
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cbvalw.5 |
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Ref | Expression |
---|---|
cbvalw |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cbvalw.1 |
. . 3
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2 | cbvalw.2 |
. . 3
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3 | cbvalw.5 |
. . . 4
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4 | 3 | biimpd 198 |
. . 3
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5 | 1, 2, 4 | cbvaliw 1673 |
. 2
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6 | cbvalw.3 |
. . 3
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7 | cbvalw.4 |
. . 3
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8 | 3 | biimprd 214 |
. . . 4
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9 | 8 | equcoms 1681 |
. . 3
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10 | 6, 7, 9 | cbvaliw 1673 |
. 2
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11 | 5, 10 | impbii 180 |
1
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Colors of variables: wff setvar class |
Syntax hints: ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1546 ax-5 1557 ax-17 1616 ax-9 1654 ax-8 1675 |
This theorem depends on definitions: df-bi 177 df-an 360 df-ex 1542 |
This theorem is referenced by: hbn1fw 1705 |
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