Theorem truimfal 1554

Description: A → identity. (Contributed by Anthony Hart, 22-Oct-2010.) (Proof shortened by Andrew Salmon, 13-May-2011.)

Assertion

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

Proof of Theorem truimfal

Step	Hyp	Ref	Expression
1		trut 1536	. 2 ⊢ (⊥ ↔ (⊤ → ⊥))
2	1	bicomi 226	1 ⊢ ((⊤ → ⊥) ↔ ⊥)

Syntax hints:   → wi 4   ↔ wb 208  ⊤wtru 1531  ⊥wfal 1542

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 1533

This theorem is referenced by: (None)