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Metamath Proof Explorer

Theorem tbtru

Description: A proposition is equivalent to itself being equivalent to T. . (Contributed by Anthony Hart, 14-Aug-2011)

Ref Expression
Assertion tbtru ( 𝜑 ↔ ( 𝜑 ↔ ⊤ ) )

Proof

Step Hyp Ref Expression
1 tru ⊢ ⊤
2 1 tbt ⊢ ( 𝜑 ↔ ( 𝜑 ↔ ⊤ ) )