Theorem falimfal 1580

Description: A → identity. (Contributed by Anthony Hart, 22-Oct-2010.) An alternate proof is possible using falim 1571 instead of id 22 but the present proof using id 22 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 22	. 2 ⊢ (⊥ → ⊥)
2	1	bitru 1563	1 ⊢ ((⊥ → ⊥) ↔ ⊤)

Syntax hints:   → wi 4   ↔ wb 208  ⊤wtru 1555  ⊥wfal 1566

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 1557

This theorem is referenced by: (None)