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Mirrors > Home > ILE Home > Th. List > cbval2 | Unicode version |
Description: Rule used to change bound variables, using implicit substitution. (Contributed by NM, 22-Dec-2003.) (Revised by Mario Carneiro, 6-Oct-2016.) (Proof shortened by Wolf Lammen, 22-Apr-2018.) |
Ref | Expression |
---|---|
cbval2.1 |
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cbval2.2 |
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cbval2.3 |
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cbval2.4 |
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cbval2.5 |
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Ref | Expression |
---|---|
cbval2 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cbval2.1 |
. . 3
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2 | 1 | nfal 1465 |
. 2
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3 | cbval2.3 |
. . 3
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4 | 3 | nfal 1465 |
. 2
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5 | nfv 1418 |
. . . . . 6
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6 | cbval2.2 |
. . . . . 6
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7 | 5, 6 | nfim 1461 |
. . . . 5
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8 | nfv 1418 |
. . . . . 6
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9 | cbval2.4 |
. . . . . 6
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10 | 8, 9 | nfim 1461 |
. . . . 5
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11 | cbval2.5 |
. . . . . . 7
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12 | 11 | expcom 109 |
. . . . . 6
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13 | 12 | pm5.74d 171 |
. . . . 5
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14 | 7, 10, 13 | cbval 1634 |
. . . 4
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15 | 19.21v 1750 |
. . . 4
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16 | 19.21v 1750 |
. . . 4
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17 | 14, 15, 16 | 3bitr3i 199 |
. . 3
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18 | 17 | pm5.74ri 170 |
. 2
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19 | 2, 4, 18 | cbval 1634 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-5 1333 ax-7 1334 ax-gen 1335 ax-ie1 1379 ax-ie2 1380 ax-8 1392 ax-4 1397 ax-17 1416 ax-i9 1420 ax-ial 1424 ax-i5r 1425 |
This theorem depends on definitions: df-bi 110 df-nf 1347 |
This theorem is referenced by: cbval2v 1795 |
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