Theorem bothfbothsame 47254

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 1554

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  47303  mdandyv1  47304  mdandyv2  47305  mdandyv3  47306  mdandyv4  47307  mdandyv5  47308  mdandyv6  47309  mdandyv7  47310  mdandyv8  47311  mdandyv9  47312  mdandyv10  47313  mdandyv11  47314  mdandyv12  47315  mdandyv13  47316  mdandyv14  47317  dandysum2p2e4  47352