Theorem aiffbtbat 43137

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.)

Hypotheses

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

Assertion

Ref	Expression
aiffbtbat	⊢ (𝜑 ↔ ⊤)

Proof of Theorem aiffbtbat

Step	Hyp	Ref	Expression
1		aiffbtbat.1	. 2 ⊢ (𝜑 ↔ 𝜓)
2		aiffbtbat.2	. 2 ⊢ (⊤ ↔ 𝜓)
3	1, 2	bitr4i 280	1 ⊢ (𝜑 ↔ ⊤)

Syntax hints:   ↔ wb 208  ⊤wtru 1534

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 209

This theorem is referenced by: (None)