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Mirrors > Home > ILE Home > Th. List > pclem6 | Unicode version |
Description: Negation inferred from embedded conjunct. (Contributed by NM, 20-Aug-1993.) (Proof rewritten by Jim Kingdon, 4-May-2018.) |
Ref | Expression |
---|---|
pclem6 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bi1 111 |
. . . . 5
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2 | pm3.4 316 |
. . . . . 6
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3 | 2 | com12 27 |
. . . . 5
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4 | 1, 3 | syl9r 67 |
. . . 4
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5 | ax-ia3 101 |
. . . . 5
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6 | bi2 121 |
. . . . 5
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7 | 5, 6 | syl9 66 |
. . . 4
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8 | 4, 7 | impbidd 118 |
. . 3
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9 | pm5.19 621 |
. . . 4
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10 | 9 | pm2.21i 574 |
. . 3
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11 | 8, 10 | syl6com 31 |
. 2
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12 | dfnot 1261 |
. 2
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13 | 11, 12 | sylibr 137 |
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-in1 544 ax-in2 545 |
This theorem depends on definitions: df-bi 110 df-tru 1245 df-fal 1248 |
This theorem is referenced by: nalset 3878 pwnss 3903 bj-nalset 9350 |
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