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Mirrors > Home > QLE Home > Th. List > negantlem2 | Unicode version |
Description: Lemma for negated antecedent identity. |
Ref | Expression |
---|---|
negant.1 |
Ref | Expression |
---|---|
negantlem2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | leo 158 | . 2 | |
2 | i1orni1 847 | . . . . . 6 | |
3 | 2 | lan 77 | . . . . 5 |
4 | 3 | ax-r1 35 | . . . 4 |
5 | an1 106 | . . . . 5 | |
6 | 5 | ax-r1 35 | . . . 4 |
7 | u1lemc6 706 | . . . . 5 | |
8 | negant.1 | . . . . . . 7 | |
9 | 8 | negantlem1 848 | . . . . . 6 |
10 | 9 | comcom 453 | . . . . 5 |
11 | 7, 10 | fh4rc 482 | . . . 4 |
12 | 4, 6, 11 | 3tr1 63 | . . 3 |
13 | ancom 74 | . . . . . . . 8 | |
14 | 8 | lan 77 | . . . . . . . 8 |
15 | u1lemaa 600 | . . . . . . . 8 | |
16 | 13, 14, 15 | 3tr2 64 | . . . . . . 7 |
17 | lear 161 | . . . . . . 7 | |
18 | 16, 17 | bltr 138 | . . . . . 6 |
19 | lear 161 | . . . . . 6 | |
20 | 18, 19 | ler2an 173 | . . . . 5 |
21 | lea 160 | . . . . . . . 8 | |
22 | ax-a1 30 | . . . . . . . 8 | |
23 | 21, 22 | lbtr 139 | . . . . . . 7 |
24 | 23 | leror 152 | . . . . . 6 |
25 | ancom 74 | . . . . . . 7 | |
26 | u1lemab 610 | . . . . . . 7 | |
27 | 25, 26 | ax-r2 36 | . . . . . 6 |
28 | df-i1 44 | . . . . . 6 | |
29 | 24, 27, 28 | le3tr1 140 | . . . . 5 |
30 | 20, 29 | letr 137 | . . . 4 |
31 | leid 148 | . . . 4 | |
32 | 30, 31 | lel2or 170 | . . 3 |
33 | 12, 32 | bltr 138 | . 2 |
34 | 1, 33 | letr 137 | 1 |
Colors of variables: term |
Syntax hints: wb 1 wle 2 wn 4 wo 6 wa 7 wt 8 wi1 12 |
This theorem was proved from axioms: ax-a1 30 ax-a2 31 ax-a3 32 ax-a4 33 ax-a5 34 ax-r1 35 ax-r2 36 ax-r4 37 ax-r5 38 ax-r3 439 |
This theorem depends on definitions: df-b 39 df-a 40 df-t 41 df-f 42 df-i1 44 df-le1 130 df-le2 131 df-c1 132 df-c2 133 |
This theorem is referenced by: negantlem4 851 |
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