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	$$⊢\phi \leftrightarrow \psi$$
	aiffbtbat.2	$$⊢\top \leftrightarrow \psi$$
Assertion	aiffbtbat	$$⊢\phi \leftrightarrow \top$$

Proof

Step	Hyp	Ref	Expression
1		aiffbtbat.1	$$⊢\phi \leftrightarrow \psi$$
2		aiffbtbat.2	$$⊢\top \leftrightarrow \psi$$
3	1 2	bitr4i	$$⊢\phi \leftrightarrow \top$$