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Mirrors > Home > ILE Home > Th. List > gencbval | Unicode version |
Description: Change of bound variable using implicit substitution. (Contributed by NM, 17-May-1996.) (Proof rewritten by Jim Kingdon, 20-Jun-2018.) |
Ref | Expression |
---|---|
gencbval.1 |
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gencbval.2 |
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gencbval.3 |
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gencbval.4 |
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Ref | Expression |
---|---|
gencbval |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | alcom 1478 |
. 2
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2 | gencbval.1 |
. . . 4
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3 | gencbval.3 |
. . . . . . 7
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4 | gencbval.2 |
. . . . . . 7
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5 | 3, 4 | imbi12d 234 |
. . . . . 6
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6 | 5 | bicomd 141 |
. . . . 5
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7 | 6 | eqcoms 2180 |
. . . 4
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8 | 2, 7 | ceqsalv 2768 |
. . 3
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9 | 8 | albii 1470 |
. 2
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10 | 19.23v 1883 |
. . . 4
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11 | gencbval.4 |
. . . . . . 7
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12 | eqcom 2179 |
. . . . . . . . . 10
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13 | 12 | biimpi 120 |
. . . . . . . . 9
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14 | 13 | adantl 277 |
. . . . . . . 8
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15 | 14 | eximi 1600 |
. . . . . . 7
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16 | 11, 15 | sylbi 121 |
. . . . . 6
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17 | pm2.04 82 |
. . . . . 6
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18 | 16, 17 | mpdi 43 |
. . . . 5
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19 | ax-1 6 |
. . . . 5
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20 | 18, 19 | impbii 126 |
. . . 4
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21 | 10, 20 | bitri 184 |
. . 3
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22 | 21 | albii 1470 |
. 2
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23 | 1, 9, 22 | 3bitr3i 210 |
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-8 1504 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-ext 2159 |
This theorem depends on definitions: df-bi 117 df-nf 1461 df-sb 1763 df-clab 2164 df-cleq 2170 df-clel 2173 df-v 2740 |
This theorem is referenced by: (None) |
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