Theorem truimtru 1590

Description: A → identity. (Contributed by Anthony Hart, 22-Oct-2010.) An alternate proof is possible using trud 1577 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 1576	1 ⊢ ((⊤ → ⊤) ↔ ⊤)

Syntax hints:   → wi 4   ↔ wb 209  ⊤wtru 1568

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 210  df-tru 1570

This theorem is referenced by: (None)