Theorem tbtru 1542

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 1538	. 2 ⊢ ⊤
2	1	tbt 368	1 ⊢ (𝜑 ↔ (𝜑 ↔ ⊤))

Syntax hints:   ↔ wb 205  ⊤wtru 1535

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 206  df-tru 1537

This theorem is referenced by:  falbitru  1564  ab0orv  4383  tgcgr4  28458  iinabrex  32489  sgn3da  34375  wl-1xor  37189  wl-1mintru1  37195  prjspvs  42264  aistia  46512