Theorem bothfbothsame 47914

Description: Given both a, b are equivalent to ⊥, there exists a proof for a is the same as b. (Contributed by Jarvin Udandy, 31-Aug-2016.)

Hypotheses

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

Assertion

Ref	Expression
bothfbothsame	⊢ (𝜑 ↔ 𝜓)

Proof of Theorem bothfbothsame

Step	Hyp	Ref	Expression
1		bothfbothsame.1	. 2 ⊢ (𝜑 ↔ ⊥)
2		bothfbothsame.2	. 2 ⊢ (𝜓 ↔ ⊥)
3	1, 2	bitr4i 281	1 ⊢ (𝜑 ↔ 𝜓)

This proof depends on syntax axioms:   ↔ wb 209  ⊥wfal 1582

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:  mdandyv0  47963  mdandyv1  47964  mdandyv2  47965  mdandyv3  47966  mdandyv4  47967  mdandyv5  47968  mdandyv6  47969  mdandyv7  47970  mdandyv8  47971  mdandyv9  47972  mdandyv10  47973  mdandyv11  47974  mdandyv12  47975  mdandyv13  47976  mdandyv14  47977  dandysum2p2e4  48012