Theorem falantru 1605

Description: A ∧ identity. (Contributed by Anthony Hart, 22-Oct-2010.)

Assertion

Ref	Expression
falantru	⊢ ((⊥ ∧ ⊤) ↔ ⊥)

Proof of Theorem falantru

Step	Hyp	Ref	Expression
1		fal 1584	. . 3 ⊢ ¬ ⊥
2	1	intnanr 493	. 2 ⊢ ¬ (⊥ ∧ ⊤)
3	2	bifal 1586	1 ⊢ ((⊥ ∧ ⊤) ↔ ⊥)

This proof depends on syntax axioms:   ↔ wb 209   ∧ wa 401  ⊤wtru 1571  ⊥wfal 1582

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-an 402  df-tru 1573  df-fal 1583

This theorem is used by: (None)