Theorem tbtru 1551

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 1547	. 2 ⊢ ⊤
2	1	tbt 373	1 ⊢ (𝜑 ↔ (𝜑 ↔ ⊤))

Syntax hints:   ↔ wb 209  ⊤wtru 1544

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 210  df-tru 1546

This theorem is referenced by:  falbitru  1573  ab0orv  4279  tgcgr4  26576  iinabrex  30581  sgn3da  32174  wl-1xor  35339  wl-1mintru1  35345  prjspvs  40098  aistia  44007