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Mirrors > Home > ILE Home > Th. List > dveeq2 | Unicode version |
Description: Quantifier introduction when one pair of variables is distinct. (Contributed by NM, 2-Jan-2002.) |
Ref | Expression |
---|---|
dveeq2 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax-i12 1468 |
. . . . 5
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2 | orcom 700 |
. . . . . 6
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3 | 2 | orbi2i 734 |
. . . . 5
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4 | 1, 3 | mpbi 144 |
. . . 4
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5 | orass 739 |
. . . 4
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6 | 4, 5 | mpbir 145 |
. . 3
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7 | orel2 698 |
. . 3
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8 | 6, 7 | mpi 15 |
. 2
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9 | ax16 1767 |
. . 3
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10 | sp 1471 |
. . 3
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11 | 9, 10 | jaoi 688 |
. 2
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12 | 8, 11 | syl 14 |
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-in2 587 ax-io 681 ax-5 1406 ax-7 1407 ax-gen 1408 ax-ie1 1452 ax-ie2 1453 ax-8 1465 ax-10 1466 ax-11 1467 ax-i12 1468 ax-4 1470 ax-17 1489 ax-i9 1493 ax-ial 1497 |
This theorem depends on definitions: df-bi 116 df-nf 1420 df-sb 1719 |
This theorem is referenced by: nd5 1772 ax11v2 1774 dveeq1 1970 |
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