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Mirrors > Home > ILE Home > Th. List > cbv1h | Unicode version |
Description: Rule used to change bound variables, using implicit substitution. (Contributed by NM, 5-Aug-1993.) (Proof shortened by Wolf Lammen, 13-May-2018.) |
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 | nfa1 1522 |
. 2
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2 | nfa2 1559 |
. 2
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3 | sp 1489 |
. . . . 5
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4 | 3 | sps 1518 |
. . . 4
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5 | cbv1h.1 |
. . . 4
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6 | 4, 5 | syl 14 |
. . 3
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7 | 2, 6 | nfd 1504 |
. 2
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8 | cbv1h.2 |
. . . 4
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9 | 4, 8 | syl 14 |
. . 3
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10 | 1, 9 | nfd 1504 |
. 2
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11 | cbv1h.3 |
. . 3
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12 | 4, 11 | syl 14 |
. 2
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13 | 1, 2, 7, 10, 12 | cbv1 1723 |
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-4 1488 ax-i9 1511 ax-ial 1515 ax-i5r 1516 |
This theorem depends on definitions: df-bi 116 df-nf 1438 |
This theorem is referenced by: cbv2h 1725 |
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