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Mirrors > Home > ILE Home > Th. List > cbvexh | Unicode version |
Description: Rule used to change bound variables, using implicit substitition. (Contributed by NM, 5-Aug-1993.) (Revised by Mario Carneiro, 3-Feb-2015.) |
Ref | Expression |
---|---|
cbvexh.1 |
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cbvexh.2 |
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cbvexh.3 |
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Ref | Expression |
---|---|
cbvexh |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cbvexh.2 |
. . . 4
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2 | 1 | hbex 1647 |
. . 3
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3 | cbvexh.1 |
. . . . 5
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4 | cbvexh.3 |
. . . . . . 7
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5 | 4 | bicomd 141 |
. . . . . 6
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6 | 5 | equcoms 1719 |
. . . . 5
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7 | 3, 6 | equsex 1739 |
. . . 4
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8 | simpr 110 |
. . . . 5
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9 | 8 | eximi 1611 |
. . . 4
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10 | 7, 9 | sylbir 135 |
. . 3
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11 | 2, 10 | exlimih 1604 |
. 2
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12 | 3 | hbex 1647 |
. . 3
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13 | 1, 4 | equsex 1739 |
. . . 4
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14 | simpr 110 |
. . . . 5
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15 | 14 | eximi 1611 |
. . . 4
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16 | 13, 15 | sylbir 135 |
. . 3
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17 | 12, 16 | exlimih 1604 |
. 2
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18 | 11, 17 | impbii 126 |
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 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 |
This theorem depends on definitions: df-bi 117 |
This theorem is referenced by: cbvex 1767 sb8eh 1866 cbvexv 1930 euf 2043 mopick 2116 |
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