Theorem bothtbothsame

Description: Given both a, b are equivalent to T. , there exists a proof for a is the same as b. (Contributed by Jarvin Udandy, 31-Aug-2016)

	Ref	Expression
Hypotheses	bothtbothsame.1	⊢ ( 𝜑 ↔ ⊤ )
	bothtbothsame.2	⊢ ( 𝜓 ↔ ⊤ )
Assertion	bothtbothsame	⊢ ( 𝜑 ↔ 𝜓 )

Proof

Step	Hyp	Ref	Expression
1		bothtbothsame.1	⊢ ( 𝜑 ↔ ⊤ )
2		bothtbothsame.2	⊢ ( 𝜓 ↔ ⊤ )
3	1 2	bitr4i	⊢ ( 𝜑 ↔ 𝜓 )