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Mirrors > Home > ILE Home > Th. List > dveeq2or | Unicode version |
Description: Quantifier introduction
when one pair of variables is distinct. Like
dveeq2 1815 but connecting ![]() ![]() ![]() ![]() ![]() |
Ref | Expression |
---|---|
dveeq2or |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax12or 1508 |
. . . . . 6
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2 | orass 767 |
. . . . . 6
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3 | 1, 2 | mpbir 146 |
. . . . 5
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4 | pm1.4 727 |
. . . . . 6
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5 | 4 | orim1i 760 |
. . . . 5
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6 | 3, 5 | ax-mp 5 |
. . . 4
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7 | orass 767 |
. . . 4
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8 | 6, 7 | mpbi 145 |
. . 3
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9 | ax16 1813 |
. . . . . 6
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10 | 9 | a5i 1543 |
. . . . 5
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11 | id 19 |
. . . . 5
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12 | 10, 11 | jaoi 716 |
. . . 4
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13 | 12 | orim2i 761 |
. . 3
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14 | 8, 13 | ax-mp 5 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
15 | df-nf 1461 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
16 | 15 | biimpri 133 |
. . 3
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17 | 16 | orim2i 761 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
18 | 14, 17 | ax-mp 5 |
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-io 709 ax-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-10 1505 ax-11 1506 ax-i12 1507 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 |
This theorem depends on definitions: df-bi 117 df-nf 1461 df-sb 1763 |
This theorem is referenced by: equs5or 1830 sbal1yz 2001 copsexg 4244 |
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