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Mirrors > Home > NFE Home > Th. List > cbv1h | Unicode version |
Description: Rule used to change bound variables, using implicit substitution. (Contributed by NM, 5-Aug-1993.) |
Ref | Expression |
---|---|
cbv1h.1 |
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cbv1h.2 |
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cbv1h.3 |
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Ref | Expression |
---|---|
cbv1h |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cbv1h.1 |
. . . . 5
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2 | 1 | sps 1754 |
. . . 4
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3 | 2 | al2imi 1561 |
. . 3
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4 | ax-7 1734 |
. . 3
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5 | 3, 4 | syl6 29 |
. 2
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6 | cbv1h.3 |
. . . . . . . 8
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7 | 6 | com23 72 |
. . . . . . 7
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8 | cbv1h.2 |
. . . . . . 7
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9 | 7, 8 | syl6d 64 |
. . . . . 6
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10 | 9 | al2imi 1561 |
. . . . 5
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11 | ax9o 1950 |
. . . . 5
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12 | 10, 11 | syl6 29 |
. . . 4
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13 | 12 | al2imi 1561 |
. . 3
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14 | 13 | a7s 1735 |
. 2
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15 | 5, 14 | syld 40 |
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 ax-6 1729 ax-7 1734 ax-11 1746 ax-12 1925 |
This theorem depends on definitions: df-bi 177 df-an 360 df-tru 1319 df-ex 1542 df-nf 1545 |
This theorem is referenced by: cbv1 1979 cbv2h 1980 cbv3h 1983 |
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