Theorem tbtru 1548

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 1544	. 2 ⊢ ⊤
2	1	tbt 369	1 ⊢ (𝜑 ↔ (𝜑 ↔ ⊤))

Syntax hints:   ↔ wb 206  ⊤wtru 1541

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 207  df-tru 1543

This theorem is referenced by:  falbitru  1570  ab0orv  4358  tgcgr4  28510  iinabrex  32550  sgn3da  32813  wl-1xor  37500  wl-1mintru1  37506  prjspvs  42633  lambert0  46919  lamberte  46920  aistia  46926  isinito2lem  49383