Theorem falimfal 1563

Description: A → identity. (Contributed by Anthony Hart, 22-Oct-2010.) An alternate proof is possible using falim 1554 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 1546	1 ⊢ ((⊥ → ⊥) ↔ ⊤)

Syntax hints:   → wi 4   ↔ wb 208  ⊤wtru 1538  ⊥wfal 1549

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)