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Mirrors > Home > ILE Home > Th. List > dfif3 | Unicode version |
Description: Alternate definition of
the conditional operator df-if 3480. Note that
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Ref | Expression |
---|---|
dfif3.1 |
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Ref | Expression |
---|---|
dfif3 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dfif6 3481 |
. 2
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2 | dfif3.1 |
. . . . . 6
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3 | biidd 171 |
. . . . . . 7
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4 | 3 | cbvabv 2265 |
. . . . . 6
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5 | 2, 4 | eqtri 2161 |
. . . . 5
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6 | 5 | ineq2i 3279 |
. . . 4
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7 | dfrab3 3357 |
. . . 4
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8 | 6, 7 | eqtr4i 2164 |
. . 3
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9 | dfrab3 3357 |
. . . 4
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10 | notab 3351 |
. . . . . 6
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11 | 5 | difeq2i 3196 |
. . . . . 6
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12 | 10, 11 | eqtr4i 2164 |
. . . . 5
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13 | 12 | ineq2i 3279 |
. . . 4
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14 | 9, 13 | eqtr2i 2162 |
. . 3
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15 | 8, 14 | uneq12i 3233 |
. 2
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16 | 1, 15 | eqtr4i 2164 |
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 105 ax-ia2 106 ax-ia3 107 ax-in1 604 ax-in2 605 ax-io 699 ax-5 1424 ax-7 1425 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1483 ax-10 1484 ax-11 1485 ax-i12 1486 ax-bndl 1487 ax-4 1488 ax-17 1507 ax-i9 1511 ax-ial 1515 ax-i5r 1516 ax-ext 2122 |
This theorem depends on definitions: df-bi 116 df-tru 1335 df-fal 1338 df-nf 1438 df-sb 1737 df-clab 2127 df-cleq 2133 df-clel 2136 df-nfc 2271 df-ral 2422 df-rab 2426 df-v 2691 df-dif 3078 df-un 3080 df-in 3082 df-if 3480 |
This theorem is referenced by: (None) |
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