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Mirrors > Home > ILE Home > Th. List > 2gencl | Unicode version |
Description: Implicit substitution for class with embedded variable. (Contributed by NM, 17-May-1996.) |
Ref | Expression |
---|---|
2gencl.1 |
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2gencl.2 |
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2gencl.3 |
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2gencl.4 |
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2gencl.5 |
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Ref | Expression |
---|---|
2gencl |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 2gencl.2 |
. . . 4
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2 | df-rex 2312 |
. . . 4
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3 | 1, 2 | bitri 173 |
. . 3
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4 | 2gencl.4 |
. . . 4
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5 | 4 | imbi2d 219 |
. . 3
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6 | 2gencl.1 |
. . . . . 6
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7 | df-rex 2312 |
. . . . . 6
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8 | 6, 7 | bitri 173 |
. . . . 5
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9 | 2gencl.3 |
. . . . . 6
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10 | 9 | imbi2d 219 |
. . . . 5
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11 | 2gencl.5 |
. . . . . 6
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12 | 11 | ex 108 |
. . . . 5
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13 | 8, 10, 12 | gencl 2586 |
. . . 4
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14 | 13 | com12 27 |
. . 3
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15 | 3, 5, 14 | gencl 2586 |
. 2
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16 | 15 | impcom 116 |
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-gen 1338 ax-ie2 1383 ax-17 1419 |
This theorem depends on definitions: df-bi 110 df-rex 2312 |
This theorem is referenced by: 3gencl 2588 axaddrcl 6941 axmulrcl 6943 axpre-apti 6959 axpre-mulgt0 6961 uzin2 9586 |
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