Theorem dftru2 1292

Description: An alternate definition of "true". (Contributed by Anthony Hart, 13-Oct-2010.) (Revised by BJ, 12-Jul-2019.) (New usage is discouraged.)

Assertion

Ref	Expression
dftru2	⊢ (⊤ ↔ (𝜑 → 𝜑))

Proof of Theorem dftru2

Step	Hyp	Ref	Expression
1		tru 1288	. 2 ⊢ ⊤
2		id 19	. 2 ⊢ (𝜑 → 𝜑)
3	1, 2	2th 172	1 ⊢ (⊤ ↔ (𝜑 → 𝜑))

Syntax hints:   → wi 4   ↔ wb 103  ⊤wtru 1285

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106

This theorem depends on definitions:  df-bi 115  df-tru 1287

This theorem is referenced by: (None)