Theorem truimfal 1593

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 1575	. 2 ⊢ (⊥ ↔ (⊤ → ⊥))
2	1	bicomi 227	1 ⊢ ((⊤ → ⊥) ↔ ⊥)

This proof depends on syntax axioms:   → wi 4   ↔ wb 209  ⊤wtru 1570  ⊥wfal 1581

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 210  df-tru 1572

This theorem is used by: (None)