Theorem tbtru 1545

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 1541	. 2 ⊢ ⊤
2	1	tbt 372	1 ⊢ (𝜑 ↔ (𝜑 ↔ ⊤))

Syntax hints:   ↔ wb 208  ⊤wtru 1538

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 209  df-tru 1540

This theorem is referenced by:  falbitru  1567  tgcgr4  26319  sgn3da  31801  prjspvs  39267  aistia  43140