Theorem dftru2 1410

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 1406	. 2 ⊢ ⊤
2		id 19	. 2 ⊢ (𝜑 → 𝜑)
3	1, 2	2th 174	1 ⊢ (⊤ ↔ (𝜑 → 𝜑))

This proof depends on syntax axioms:   → wi 4   ↔ wb 105  ⊤wtru 1403

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

This proof depends on definitions:  df-bi 117  df-tru 1405

This theorem is used by: (None)