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Mirrors > Home > QLE Home > Th. List > negantlem3 | Unicode version |
Description: Lemma for negated antecedent identity. |
Ref | Expression |
---|---|
negant.1 |
Ref | Expression |
---|---|
negantlem3 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | leo 158 | . . . 4 | |
2 | df-i1 44 | . . . . . 6 | |
3 | 2 | ax-r1 35 | . . . . 5 |
4 | negant.1 | . . . . 5 | |
5 | 3, 4 | ax-r2 36 | . . . 4 |
6 | 1, 5 | lbtr 139 | . . 3 |
7 | 6 | leran 153 | . 2 |
8 | lea 160 | . . . 4 | |
9 | 8 | leror 152 | . . 3 |
10 | u1lemab 610 | . . 3 | |
11 | df-i1 44 | . . . 4 | |
12 | ax-a1 30 | . . . . . 6 | |
13 | 12 | ax-r5 38 | . . . . 5 |
14 | 13 | ax-r1 35 | . . . 4 |
15 | 11, 14 | ax-r2 36 | . . 3 |
16 | 9, 10, 15 | le3tr1 140 | . 2 |
17 | 7, 16 | letr 137 | 1 |
Colors of variables: term |
Syntax hints: wb 1 wle 2 wn 4 wo 6 wa 7 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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