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Mirrors > Home > QLE Home > Th. List > i3le | Unicode version |
Description: L.e. to Kalmbach implication. |
Ref | Expression |
---|---|
i3le.1 |
Ref | Expression |
---|---|
i3le |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ancom 74 | . . . 4 | |
2 | i3le.1 | . . . . . 6 | |
3 | 2 | i3lem3 506 | . . . . 5 |
4 | 2 | i3lem4 507 | . . . . . 6 |
5 | 4 | ran 78 | . . . . 5 |
6 | ancom 74 | . . . . 5 | |
7 | 3, 5, 6 | 3tr2 64 | . . . 4 |
8 | an1 106 | . . . 4 | |
9 | 1, 7, 8 | 3tr2 64 | . . 3 |
10 | 9 | df2le1 135 | . 2 |
11 | 10 | lecon1 155 | 1 |
Colors of variables: term |
Syntax hints: wb 1 wle 2 wn 4 wo 6 wa 7 wt 8 wi3 14 |
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-i3 46 df-le1 130 df-le2 131 df-c1 132 df-c2 133 |
This theorem is referenced by: binr1 517 binr2 518 binr3 519 i3ri3 538 i3li3 539 i32i3 540 u3lemle2 717 |
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