Theorem truimtru 1593

Description: A → identity. (Contributed by Anthony Hart, 22-Oct-2010.) An alternate proof is possible using trud 1580 instead of id 23 but the principle of identity id 23 is more basic, and the present proof indicates that the result still holds in relevance logic. (Proof modification is discouraged.)

Assertion

Ref	Expression
truimtru	⊢ ((⊤ → ⊤) ↔ ⊤)

Proof of Theorem truimtru

Step	Hyp	Ref	Expression
1		id 23	. 2 ⊢ (⊤ → ⊤)
2	1	bitru 1579	1 ⊢ ((⊤ → ⊤) ↔ ⊤)

This proof depends on syntax axioms:   → wi 4   ↔ wb 209  ⊤wtru 1571

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

This proof depends on definitions:  df-bi 210  df-tru 1573

This theorem is used by: (None)