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Mirrors > Home > QLE Home > Th. List > wdid0id1 | Unicode version |
Description: Show a quantum identity that follows from classical identity in a WDOL. |
Ref | Expression |
---|---|
wdid0id5.1 |
Ref | Expression |
---|---|
wdid0id1 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-id1 50 | . 2 | |
2 | df-id0 49 | . . . . 5 | |
3 | 2 | ax-r1 35 | . . . 4 |
4 | wdid0id5.1 | . . . 4 | |
5 | 3, 4 | ax-r2 36 | . . 3 |
6 | wancom 203 | . . . . . . . 8 | |
7 | wa2 192 | . . . . . . . . . 10 | |
8 | 7 | wlan 370 | . . . . . . . . 9 |
9 | wa4 194 | . . . . . . . . . 10 | |
10 | 9 | wleoa 376 | . . . . . . . . 9 |
11 | 8, 10 | wr2 371 | . . . . . . . 8 |
12 | 6, 11 | wr2 371 | . . . . . . 7 |
13 | 12 | wr1 197 | . . . . . 6 |
14 | wddi3 1107 | . . . . . . 7 | |
15 | 14 | wr1 197 | . . . . . 6 |
16 | 13, 15 | wr2 371 | . . . . 5 |
17 | wa2 192 | . . . . 5 | |
18 | 16, 17 | w2an 373 | . . . 4 |
19 | biid 116 | . . . 4 | |
20 | wancom 203 | . . . 4 | |
21 | 18, 19, 20 | w3tr1 374 | . . 3 |
22 | 5, 21 | wwbmp 205 | . 2 |
23 | 1, 22 | ax-r2 36 | 1 |
Colors of variables: term |
Syntax hints: wb 1 wn 4 wo 6 wa 7 wt 8 wid0 17 wid1 18 |
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-wom 361 ax-wdol 1102 |
This theorem depends on definitions: df-b 39 df-a 40 df-t 41 df-f 42 df-i1 44 df-i2 45 df-id0 49 df-id1 50 df-le 129 df-le1 130 df-le2 131 df-cmtr 134 |
This theorem is referenced by: wddi-1 1116 |
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