Theorem tbtru 1324

Description: If something is true, it outputs ⊤. (Contributed by Anthony Hart, 14-Aug-2011.)

Assertion

Ref	Expression
tbtru	⊢ (φ ↔ (φ ↔ ⊤ ))

Proof of Theorem tbtru

Step	Hyp	Ref	Expression
1		tru 1321	. 2 ⊢ ⊤
2	1	tbt 333	1 ⊢ (φ ↔ (φ ↔ ⊤ ))

This proof depends on syntax axioms:   ↔ wb 176   ⊤ wtru 1316

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

This proof depends on definitions:  df-bi 177  df-tru 1319

This theorem is used by: (None)