Theorem truimtru 1560

Description: A → identity. (Contributed by Anthony Hart, 22-Oct-2010.) An alternate proof is possible using trud 1547 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 1546	1 ⊢ ((⊤ → ⊤) ↔ ⊤)

Syntax hints:   → wi 4   ↔ wb 208  ⊤wtru 1538

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 209  df-tru 1540

This theorem is referenced by: (None)