Theorem truimtru 1562

Description: A → identity. (Contributed by Anthony Hart, 22-Oct-2010.) An alternate proof is possible using trud 1549 instead of id 22 but the principle of identity id 22 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 22	. 2 ⊢ (⊤ → ⊤)
2	1	bitru 1548	1 ⊢ ((⊤ → ⊤) ↔ ⊤)

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)