Theorem dftru2 1544

Description: An alternate definition of "true" (see comment of df-tru 1542). The associated justification theorem is monothetic 265. (Contributed by Anthony Hart, 13-Oct-2010.) (Revised by BJ, 12-Jul-2019.) Use tru 1543 instead. (New usage is discouraged.)

Assertion

Ref	Expression
dftru2	⊢ (⊤ ↔ (𝜑 → 𝜑))

Proof of Theorem dftru2

Step	Hyp	Ref	Expression
1		tru 1543	. 2 ⊢ ⊤
2		id 22	. 2 ⊢ (𝜑 → 𝜑)
3	1, 2	2th 263	1 ⊢ (⊤ ↔ (𝜑 → 𝜑))

Syntax hints:   → wi 4   ↔ wb 205  ⊤wtru 1540

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 1542

This theorem is referenced by: (None)