Theorem aiffbtbat

Description: Given a is equivalent to b, T. is equivalent to b. there exists a proof for a is equivalent to T. (Contributed by Jarvin Udandy, 29-Aug-2016)

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

Proof

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