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 v a_|_) = (b v b_|_)

Proof of Theorem tt

Step	Hyp	Ref	Expression
1		ax-a4 32	. . . 4 ((b v b_|_) v (a v a_|_)) = (a v a_|_)
2	1	ax-r1 34	. . 3 (a v a_|_) = ((b v b_|_) v (a v a_|_))
3		ax-a2 30	. . 3 ((b v b_|_) v (a v a_|_)) = ((a v a_|_) v (b v b_|_))
4	2, 3	ax-r2 35	. 2 (a v a_|_) = ((a v a_|_) v (b v b_|_))
5		ax-a4 32	. 2 ((a v a_|_) v (b v b_|_)) = (b v b_|_)
6	4, 5	ax-r2 35	1 (a v a_|_) = (b v b_|_)

Syntax hints:   = wb 1  _|_wn 4   v wo 6

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

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