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Mirrors > Home > ILE Home > Th. List > eqvinc | Unicode version |
Description: A variable introduction law for class equality. (Contributed by NM, 14-Apr-1995.) (Proof shortened by Andrew Salmon, 8-Jun-2011.) |
Ref | Expression |
---|---|
eqvinc.1 |
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Ref | Expression |
---|---|
eqvinc |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqvinc.1 |
. . . . 5
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2 | 1 | isseti 2628 |
. . . 4
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3 | ax-1 5 |
. . . . . 6
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4 | eqtr 2106 |
. . . . . . 7
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5 | 4 | ex 114 |
. . . . . 6
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6 | 3, 5 | jca 301 |
. . . . 5
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7 | 6 | eximi 1537 |
. . . 4
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8 | pm3.43 570 |
. . . . 5
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9 | 8 | eximi 1537 |
. . . 4
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10 | 2, 7, 9 | mp2b 8 |
. . 3
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11 | 10 | 19.37aiv 1611 |
. 2
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12 | eqtr2 2107 |
. . 3
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13 | 12 | exlimiv 1535 |
. 2
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14 | 11, 13 | impbii 125 |
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 105 ax-ia2 106 ax-ia3 107 ax-5 1382 ax-gen 1384 ax-ie1 1428 ax-ie2 1429 ax-8 1441 ax-4 1446 ax-17 1465 ax-i9 1469 ax-ial 1473 ax-ext 2071 |
This theorem depends on definitions: df-bi 116 df-nf 1396 df-sb 1694 df-clab 2076 df-cleq 2082 df-clel 2085 df-v 2622 |
This theorem is referenced by: eqvincf 2743 |
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