Theorem bothfbothsame 46885

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 278	1 ⊢ (𝜑 ↔ 𝜓)

Syntax hints:   ↔ wb 206  ⊥wfal 1552

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 207

This theorem is referenced by:  mdandyv0  46934  mdandyv1  46935  mdandyv2  46936  mdandyv3  46937  mdandyv4  46938  mdandyv5  46939  mdandyv6  46940  mdandyv7  46941  mdandyv8  46942  mdandyv9  46943  mdandyv10  46944  mdandyv11  46945  mdandyv12  46946  mdandyv13  46947  mdandyv14  46948  dandysum2p2e4  46983