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Mirrors > Home > QLE Home > Th. List > lem3.4.4 | GIF version |
Description: Equation 3.12 of [PavMeg1999] p. 9. (Contributed by Roy F. Longton, 29-Jun-2005.) (Revised by Roy F. Longton, 3-Jul-2005.) |
Ref | Expression |
---|---|
lem3.4.4.1 | (a →2 b) = 1 |
lem3.4.4.2 | (b →2 a) = 1 |
Ref | Expression |
---|---|
lem3.4.4 | (a ≡5 b) = 1 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | lem3.4.4.2 | . . . 4 (b →2 a) = 1 | |
2 | 1 | lem3.3.4 1053 | . . 3 (a →2 (a ≡5 b)) = (a ≡5 b) |
3 | 2 | ax-r1 35 | . 2 (a ≡5 b) = (a →2 (a ≡5 b)) |
4 | lem3.4.4.1 | . . 3 (a →2 b) = 1 | |
5 | 4 | lem3.4.3 1076 | . 2 (a →2 (a ≡5 b)) = 1 |
6 | 3, 5 | ax-r2 36 | 1 (a ≡5 b) = 1 |
Colors of variables: term |
Syntax hints: = wb 1 1wt 8 →2 wi2 13 ≡5 wid5 22 |
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 |
This theorem depends on definitions: df-a 40 df-t 41 df-f 42 df-i1 44 df-i2 45 df-le1 130 df-le2 131 df-id5 1047 |
This theorem is referenced by: lem3.4.6 1079 |
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