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Mirrors > Home > MPE Home > Th. List > cbv2h | Structured version Visualization version Unicode version |
Description: Rule used to change bound variables, using implicit substitution. (Contributed by NM, 11-May-1993.) |
Ref | Expression |
---|---|
cbv2h.1 |
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cbv2h.2 |
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cbv2h.3 |
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Ref | Expression |
---|---|
cbv2h |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cbv2h.1 |
. . 3
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2 | cbv2h.2 |
. . 3
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3 | cbv2h.3 |
. . . 4
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4 | biimp 198 |
. . . 4
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5 | 3, 4 | syl6 34 |
. . 3
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6 | 1, 2, 5 | cbv1h 2122 |
. 2
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7 | equcomi 1872 |
. . . . 5
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8 | biimpr 203 |
. . . . 5
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9 | 7, 3, 8 | syl56 35 |
. . . 4
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10 | 2, 1, 9 | cbv1h 2122 |
. . 3
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11 | 10 | alcoms 1932 |
. 2
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12 | 6, 11 | impbid 195 |
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 1680 ax-4 1693 ax-5 1769 ax-6 1816 ax-7 1862 ax-10 1926 ax-11 1931 ax-12 1944 ax-13 2102 |
This theorem depends on definitions: df-bi 190 df-an 377 df-ex 1675 df-nf 1679 |
This theorem is referenced by: cbv2 2124 eujustALT 2313 |
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