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Mirrors > Home > QLE Home > Th. List > comi31 | Unicode version |
Description: Commutation theorem. |
Ref | Expression |
---|---|
comi31 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | coman1 185 | . . . . . . 7 | |
2 | 1 | comcom 453 | . . . . . 6 |
3 | 2 | comcom2 183 | . . . . 5 |
4 | 3 | comcom5 458 | . . . 4 |
5 | coman1 185 | . . . . . . 7 | |
6 | 5 | comcom 453 | . . . . . 6 |
7 | 6 | comcom2 183 | . . . . 5 |
8 | 7 | comcom5 458 | . . . 4 |
9 | 4, 8 | com2or 483 | . . 3 |
10 | coman1 185 | . . . 4 | |
11 | 10 | comcom 453 | . . 3 |
12 | 9, 11 | com2or 483 | . 2 |
13 | df-i3 46 | . . 3 | |
14 | 13 | ax-r1 35 | . 2 |
15 | 12, 14 | cbtr 182 | 1 |
Colors of variables: term |
Syntax hints: wc 3 wn 4 wo 6 wa 7 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: i3abs3 524 u3lemc1 682 u3lemc5 698 u3lem1 736 u3lem2 746 u3lem5 763 u3lem6 767 u3lem7 774 u3lem8 783 u3lem9 784 u3lem13a 789 u3lem13b 790 |
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