Theorem bothtbothsame 46204

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 205  ⊤wtru 1535

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:  mdandyv1  46255  mdandyv2  46256  mdandyv3  46257  mdandyv4  46258  mdandyv5  46259  mdandyv6  46260  mdandyv7  46261  mdandyv8  46262  mdandyv9  46263  mdandyv10  46264  mdandyv11  46265  mdandyv12  46266  mdandyv13  46267  mdandyv14  46268  mdandyv15  46269  dandysum2p2e4  46303