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Mirrors > Home > ILE Home > Th. List > pwntru | Unicode version |
Description: A slight strengthening of pwtrufal 13365. (Contributed by Mario Carneiro and Jim Kingdon, 12-Sep-2023.) |
Ref | Expression |
---|---|
pwntru |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | simpr 109 |
. . . 4
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2 | 1 | neneqd 2330 |
. . 3
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3 | simpll 519 |
. . . . . 6
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4 | simpl 108 |
. . . . . . . . . 10
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5 | 4 | sselda 3102 |
. . . . . . . . 9
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6 | elsni 3550 |
. . . . . . . . 9
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7 | 5, 6 | syl 14 |
. . . . . . . 8
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8 | simpr 109 |
. . . . . . . 8
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9 | 7, 8 | eqeltrrd 2218 |
. . . . . . 7
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10 | 9 | snssd 3673 |
. . . . . 6
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11 | 3, 10 | eqssd 3119 |
. . . . 5
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12 | 11 | ex 114 |
. . . 4
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13 | 12 | exlimdv 1792 |
. . 3
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14 | 2, 13 | mtod 653 |
. 2
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15 | notm0 3388 |
. 2
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16 | 14, 15 | sylib 121 |
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-ne 2310 df-v 2691 df-dif 3078 df-in 3082 df-ss 3089 df-nul 3369 df-sn 3538 |
This theorem is referenced by: exmid1dc 4131 exmid1stab 13368 |
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