Theorem bothfbothsame 46282

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 205  ⊥wfal 1546

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 206

This theorem is referenced by:  mdandyv0  46331  mdandyv1  46332  mdandyv2  46333  mdandyv3  46334  mdandyv4  46335  mdandyv5  46336  mdandyv6  46337  mdandyv7  46338  mdandyv8  46339  mdandyv9  46340  mdandyv10  46341  mdandyv11  46342  mdandyv12  46343  mdandyv13  46344  mdandyv14  46345  dandysum2p2e4  46380