Theorem tbtru 1412

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

Assertion

Ref	Expression
tbtru	⊢ (𝜑 ↔ (𝜑 ↔ ⊤))

Proof of Theorem tbtru

Step	Hyp	Ref	Expression
1		tru 1406	. 2 ⊢ ⊤
2	1	tbt 247	1 ⊢ (𝜑 ↔ (𝜑 ↔ ⊤))

This proof depends on syntax axioms:   ↔ wb 105  ⊤wtru 1403

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

This proof depends on definitions:  df-bi 117  df-tru 1405

This theorem is used by: (None)