Theorem truimfal 1345

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 1321	. . 3 ⊢ ⊤
2	1	a1bi 327	. 2 ⊢ ( ⊥ ↔ ( ⊤ → ⊥ ))
3	2	bicomi 193	1 ⊢ (( ⊤ → ⊥ ) ↔ ⊥ )

This proof depends on syntax axioms:   → wi 4   ↔ wb 176   ⊤ wtru 1316   ⊥ wfal 1317

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

This proof depends on definitions:  df-bi 177  df-tru 1319

This theorem is used by: (None)