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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 1541 |
. 2
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2 | nfa2 1579 |
. 2
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3 | sp 1511 |
. . . . 5
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4 | 3 | sps 1537 |
. . . 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 1523 |
. 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 1523 |
. 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 1745 |
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 106 ax-ia2 107 ax-ia3 108 ax-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-4 1510 ax-i9 1530 ax-ial 1534 ax-i5r 1535 |
This theorem depends on definitions: df-bi 117 df-nf 1461 |
This theorem is referenced by: cbv2h 1748 |
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