Theorem tbtru 1577

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 1573	. 2 ⊢ ⊤
2	1	tbt 372	1 ⊢ (𝜑 ↔ (𝜑 ↔ ⊤))

This proof depends on syntax axioms:   ↔ wb 209  ⊤wtru 1570

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 210  df-tru 1572

This theorem is used by:  falbitru  1599  sgn3da  15254  tgcgr4  28994  iinabrex  33163  wl-1xor  38406  wl-1mintru1  38412  prjspvs  43639  lambert0  47937  lamberte  47938  tmachlem-agreeself  47946  aistia  47967  isinito2lem  50606