Theorem bothfbothsame

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

	Ref	Expression
Hypotheses	bothfbothsame.1	⊢ ( 𝜑 ↔ ⊥ )
	bothfbothsame.2	⊢ ( 𝜓 ↔ ⊥ )
Assertion	bothfbothsame	⊢ ( 𝜑 ↔ 𝜓 )

Proof

Step	Hyp	Ref	Expression
1		bothfbothsame.1	⊢ ( 𝜑 ↔ ⊥ )
2		bothfbothsame.2	⊢ ( 𝜓 ↔ ⊥ )
3	1 2	bitr4i	⊢ ( 𝜑 ↔ 𝜓 )