Theorem aisbbisfaisf 47667

Description: Given a is equivalent to b, b is equivalent to ⊥ there exists a proof for a is equivalent to F. (Contributed by Jarvin Udandy, 30-Aug-2016.)

Hypotheses

Ref	Expression
aisbbisfaisf.1	⊢ (𝜑 ↔ 𝜓)
aisbbisfaisf.2	⊢ (𝜓 ↔ ⊥)

Assertion

Ref	Expression
aisbbisfaisf	⊢ (𝜑 ↔ ⊥)

Proof of Theorem aisbbisfaisf

Step	Hyp	Ref	Expression
1		aisbbisfaisf.1	. 2 ⊢ (𝜑 ↔ 𝜓)
2		aisbbisfaisf.2	. 2 ⊢ (𝜓 ↔ ⊥)
3	1, 2	bitri 278	1 ⊢ (𝜑 ↔ ⊥)

This proof depends on syntax axioms:   ↔ wb 209  ⊥wfal 1581

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 210

This theorem is used by:  mdandysum2p2e4  47764