Theorem tbtru 1556

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 1552	. 2 ⊢ ⊤
2	1	tbt 371	1 ⊢ (𝜑 ↔ (𝜑 ↔ ⊤))

Syntax hints:   ↔ wb 208  ⊤wtru 1549

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 1551

This theorem is referenced by:  falbitru  1578  tgcgr4  28619  iinabrex  32660  sgn3da  32928  wl-1xor  37857  wl-1mintru1  37863  prjspvs  43073  lambert0  47362  lamberte  47363  aistia  47372  isinito2lem  50000