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Mirrors > Home > ILE Home > Th. List > pm13.183 | Unicode version |
Description: Compare theorem *13.183
in [WhiteheadRussell] p. 178. Only
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Ref | Expression |
---|---|
pm13.183 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqeq1 2046 |
. 2
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2 | eqeq2 2049 |
. . . 4
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3 | 2 | bibi1d 222 |
. . 3
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4 | 3 | albidv 1705 |
. 2
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5 | eqeq2 2049 |
. . . 4
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6 | 5 | alrimiv 1754 |
. . 3
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7 | stdpc4 1658 |
. . . 4
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8 | sbbi 1833 |
. . . . 5
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9 | eqsb3 2141 |
. . . . . . 7
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10 | 9 | bibi2i 216 |
. . . . . 6
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11 | equsb1 1668 |
. . . . . . 7
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12 | bi1 111 |
. . . . . . 7
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13 | 11, 12 | mpi 15 |
. . . . . 6
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
14 | 10, 13 | sylbi 114 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
15 | 8, 14 | sylbi 114 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
16 | 7, 15 | syl 14 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
17 | 6, 16 | impbii 117 |
. 2
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18 | 1, 4, 17 | vtoclbg 2614 |
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-io 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-bndl 1399 ax-4 1400 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 |
This theorem depends on definitions: df-bi 110 df-tru 1246 df-nf 1350 df-sb 1646 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-v 2559 |
This theorem is referenced by: mpt22eqb 5610 |
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