Theorem falimfal 1589

Description: A → identity. (Contributed by Anthony Hart, 22-Oct-2010.) An alternate proof is possible using falim 1580 instead of id 23 but the present proof using id 23 emphasizes that the result does not require the principle of explosion. (Proof modification is discouraged.)

Assertion

Ref	Expression
falimfal	⊢ ((⊥ → ⊥) ↔ ⊤)

Proof of Theorem falimfal

Step	Hyp	Ref	Expression
1		id 23	. 2 ⊢ (⊥ → ⊥)
2	1	bitru 1572	1 ⊢ ((⊥ → ⊥) ↔ ⊤)

Syntax hints:   → wi 4   ↔ wb 209  ⊤wtru 1564  ⊥wfal 1575

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 1566

This theorem is referenced by: (None)