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Mirrors > Home > QLE Home > Th. List > mlduali | Unicode version |
Description: Inference version of dual of modular law. |
Ref | Expression |
---|---|
mlduali.1 |
Ref | Expression |
---|---|
mlduali |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax-a2 31 | . . . 4 | |
2 | 1 | ran 78 | . . 3 |
3 | ancom 74 | . . 3 | |
4 | mlduali.1 | . . . 4 | |
5 | 4 | mldual2i 1125 | . . 3 |
6 | 2, 3, 5 | 3tr 65 | . 2 |
7 | ancom 74 | . . 3 | |
8 | 7 | ror 71 | . 2 |
9 | orcom 73 | . 2 | |
10 | 6, 8, 9 | 3tr 65 | 1 |
Colors of variables: term |
Syntax hints: wb 1 wle 2 wo 6 wa 7 |
This theorem was proved from axioms: ax-a1 30 ax-a2 31 ax-a3 32 ax-a5 34 ax-r1 35 ax-r2 36 ax-r4 37 ax-r5 38 ax-ml 1120 |
This theorem depends on definitions: df-a 40 df-t 41 df-f 42 df-le1 130 df-le2 131 |
This theorem is referenced by: ml3le 1127 modexp 1150 dp15lema 1152 dp35leme 1171 xdp15 1197 xxdp15 1200 xdp45lem 1202 xdp43lem 1203 xdp45 1204 xdp43 1205 3dp43 1206 testmod2 1213 testmod2expanded 1214 |
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