Theorem falimfal 1564

Description: A → identity. (Contributed by Anthony Hart, 22-Oct-2010.) An alternate proof is possible using falim 1555 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 1547	1 ⊢ ((⊥ → ⊥) ↔ ⊤)

Syntax hints:   → wi 4   ↔ wb 209  ⊤wtru 1539  ⊥wfal 1550

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 1541

This theorem is referenced by: (None)