Theorem tt 59

Description: Justification of definition df-t 40 of true (1). This shows that the definition is independent of the variable used to define it.

Assertion

Ref	Expression
tt	(a ∪ a⊥ ) = (b ∪ b⊥ )

Proof of Theorem tt

Step	Hyp	Ref	Expression
1		ax-a4 32	. . . 4 ((b ∪ b⊥ ) ∪ (a ∪ a⊥ )) = (a ∪ a⊥ )
2	1	ax-r1 34	. . 3 (a ∪ a⊥ ) = ((b ∪ b⊥ ) ∪ (a ∪ a⊥ ))
3		ax-a2 30	. . 3 ((b ∪ b⊥ ) ∪ (a ∪ a⊥ )) = ((a ∪ a⊥ ) ∪ (b ∪ b⊥ ))
4	2, 3	ax-r2 35	. 2 (a ∪ a⊥ ) = ((a ∪ a⊥ ) ∪ (b ∪ b⊥ ))
5		ax-a4 32	. 2 ((a ∪ a⊥ ) ∪ (b ∪ b⊥ )) = (b ∪ b⊥ )
6	4, 5	ax-r2 35	1 (a ∪ a⊥ ) = (b ∪ b⊥ )

Syntax hints:   = wb 1  ^⊥ wn 4   ∪ wo 6

This theorem was proved from axioms:  ax-a2 30  ax-a4 32  ax-r1 34  ax-r2 35

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