Theorem truimfal 1405

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		tru 1352	. . 3 ⊢ ⊤
2	1	a1bi 242	. 2 ⊢ (⊥ ↔ (⊤ → ⊥))
3	2	bicomi 131	1 ⊢ ((⊤ → ⊥) ↔ ⊥)

Syntax hints:   → wi 4   ↔ wb 104  ⊤wtru 1349  ⊥wfal 1353

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107

This theorem depends on definitions:  df-bi 116  df-tru 1351

This theorem is referenced by:  trubifal  1411