Theorem bothfbothsame 46930

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 1553

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  46979  mdandyv1  46980  mdandyv2  46981  mdandyv3  46982  mdandyv4  46983  mdandyv5  46984  mdandyv6  46985  mdandyv7  46986  mdandyv8  46987  mdandyv9  46988  mdandyv10  46989  mdandyv11  46990  mdandyv12  46991  mdandyv13  46992  mdandyv14  46993  dandysum2p2e4  47028