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Mirrors > Home > QLE Home > Th. List > r3a | GIF version |
Description: Orthomodular law restated. (Contributed by NM, 12-Aug-1997.) |
Ref | Expression |
---|---|
r3a.1 | 1 = (a ≡ b) |
Ref | Expression |
---|---|
r3a | a = b |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | r3a.1 | . . 3 1 = (a ≡ b) | |
2 | df-t 41 | . . 3 1 = (a ∪ a⊥ ) | |
3 | df-b 39 | . . 3 (a ≡ b) = ((a⊥ ∪ b⊥ )⊥ ∪ (a ∪ b)⊥ ) | |
4 | 1, 2, 3 | 3tr2 64 | . 2 (a ∪ a⊥ ) = ((a⊥ ∪ b⊥ )⊥ ∪ (a ∪ b)⊥ ) |
5 | 4 | ax-r3 439 | 1 a = b |
Colors of variables: term |
Syntax hints: = wb 1 ⊥ wn 4 ≡ tb 5 ∪ wo 6 1wt 8 |
This theorem was proved from axioms: ax-r1 35 ax-r2 36 ax-r3 439 |
This theorem depends on definitions: df-b 39 df-t 41 |
This theorem is referenced by: wed 441 lem3.1 443 oi3oa3lem1 732 oi3oa3 733 |
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