Theorem aiffbbtat 39717

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

Hypotheses

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

Assertion

Ref	Expression
aiffbbtat	⊢ (𝜑 ↔ ⊤)

Proof of Theorem aiffbbtat

Step	Hyp	Ref	Expression
1		aiffbbtat.1	. 2 ⊢ (𝜑 ↔ 𝜓)
2		aiffbbtat.2	. 2 ⊢ (𝜓 ↔ ⊤)
3	1, 2	bitri 263	1 ⊢ (𝜑 ↔ ⊤)

Syntax hints:   ↔ wb 195  ⊤wtru 1476

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 196

This theorem is referenced by:  dandysum2p2e4  39814  mdandysum2p2e4  39815