Theorem falantru 1573

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

Assertion

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

Proof of Theorem falantru

Step	Hyp	Ref	Expression
1		fal 1552	. . 3 ⊢ ¬ ⊥
2	1	intnanr 491	. 2 ⊢ ¬ (⊥ ∧ ⊤)
3	2	bifal 1554	1 ⊢ ((⊥ ∧ ⊤) ↔ ⊥)

Syntax hints:   ↔ wb 209   ∧ wa 399  ⊤wtru 1539  ⊥wfal 1550

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 210  df-an 400  df-tru 1541  df-fal 1551

This theorem is referenced by: (None)