Theorem bothtbothsame 44345

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 277	1 ⊢ (𝜑 ↔ 𝜓)

Syntax hints:   ↔ wb 205  ⊤wtru 1542

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  44396  mdandyv2  44397  mdandyv3  44398  mdandyv4  44399  mdandyv5  44400  mdandyv6  44401  mdandyv7  44402  mdandyv8  44403  mdandyv9  44404  mdandyv10  44405  mdandyv11  44406  mdandyv12  44407  mdandyv13  44408  mdandyv14  44409  mdandyv15  44410  dandysum2p2e4  44444