Theorem bothtbothsame 46857

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
bothtbothsame.1	⊢ (𝜑 ↔ ⊤)
bothtbothsame.2	⊢ (𝜓 ↔ ⊤)

Assertion

Ref	Expression
bothtbothsame	⊢ (𝜑 ↔ 𝜓)

Proof of Theorem bothtbothsame

Step	Hyp	Ref	Expression
1		bothtbothsame.1	. 2 ⊢ (𝜑 ↔ ⊤)
2		bothtbothsame.2	. 2 ⊢ (𝜓 ↔ ⊤)
3	1, 2	bitr4i 278	1 ⊢ (𝜑 ↔ 𝜓)

Syntax hints:   ↔ wb 206  ⊤wtru 1540

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:  mdandyv1  46908  mdandyv2  46909  mdandyv3  46910  mdandyv4  46911  mdandyv5  46912  mdandyv6  46913  mdandyv7  46914  mdandyv8  46915  mdandyv9  46916  mdandyv10  46917  mdandyv11  46918  mdandyv12  46919  mdandyv13  46920  mdandyv14  46921  mdandyv15  46922  dandysum2p2e4  46956