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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 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bi1 111 | . . . . 5 | |
2 | pm3.4 316 | . . . . . 6 | |
3 | 2 | com12 27 | . . . . 5 |
4 | 1, 3 | syl9r 67 | . . . 4 |
5 | ax-ia3 101 | . . . . 5 | |
6 | bi2 121 | . . . . 5 | |
7 | 5, 6 | syl9 66 | . . . 4 |
8 | 4, 7 | impbidd 118 | . . 3 |
9 | pm5.19 622 | . . . 4 | |
10 | 9 | pm2.21i 575 | . . 3 |
11 | 8, 10 | syl6com 31 | . 2 |
12 | dfnot 1262 | . 2 | |
13 | 11, 12 | sylibr 137 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wa 97 wb 98 wfal 1248 |
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 1246 df-fal 1249 |
This theorem is referenced by: nalset 3887 pwnss 3912 bj-nalset 10015 |
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