Theorem falantru 1575

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

Assertion

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

Proof of Theorem falantru

Step	Hyp	Ref	Expression
1		fal 1554	. . 3 ⊢ ¬ ⊥
2	1	intnanr 487	. 2 ⊢ ¬ (⊥ ∧ ⊤)
3	2	bifal 1556	1 ⊢ ((⊥ ∧ ⊤) ↔ ⊥)

Syntax hints:   ↔ wb 206   ∧ wa 395  ⊤wtru 1541  ⊥wfal 1552

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 207  df-an 396  df-tru 1543  df-fal 1553

This theorem is referenced by: (None)