Quantum Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > QLE Home > Th. List > tt | GIF version |
Description: Justification of Definition df-t 41 of true (1). This shows that the definition is independent of the variable used to define it. (Contributed by NM, 9-Aug-1997.) |
Ref | Expression |
---|---|
tt | (a ∪ a⊥ ) = (b ∪ b⊥ ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax-a4 33 | . . . 4 ((b ∪ b⊥ ) ∪ (a ∪ a⊥ )) = (a ∪ a⊥ ) | |
2 | 1 | ax-r1 35 | . . 3 (a ∪ a⊥ ) = ((b ∪ b⊥ ) ∪ (a ∪ a⊥ )) |
3 | ax-a2 31 | . . 3 ((b ∪ b⊥ ) ∪ (a ∪ a⊥ )) = ((a ∪ a⊥ ) ∪ (b ∪ b⊥ )) | |
4 | 2, 3 | ax-r2 36 | . 2 (a ∪ a⊥ ) = ((a ∪ a⊥ ) ∪ (b ∪ b⊥ )) |
5 | ax-a4 33 | . 2 ((a ∪ a⊥ ) ∪ (b ∪ b⊥ )) = (b ∪ b⊥ ) | |
6 | 4, 5 | ax-r2 36 | 1 (a ∪ a⊥ ) = (b ∪ b⊥ ) |
Colors of variables: term |
Syntax hints: = wb 1 ⊥ wn 4 ∪ wo 6 |
This theorem was proved from axioms: ax-a2 31 ax-a4 33 ax-r1 35 ax-r2 36 |
This theorem is referenced by: (None) |
Copyright terms: Public domain | W3C validator |