Theorem dftru2 1351

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 1347	. 2 ⊢ ⊤
2		id 19	. 2 ⊢ (𝜑 → 𝜑)
3	1, 2	2th 173	1 ⊢ (⊤ ↔ (𝜑 → 𝜑))

Syntax hints:   → wi 4   ↔ wb 104  ⊤wtru 1344

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107

This theorem depends on definitions:  df-bi 116  df-tru 1346

This theorem is referenced by: (None)