Theorem truanfal 1337

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

Assertion

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

Proof of Theorem truanfal

Step	Hyp	Ref	Expression
1		fal 1322	. . 3 ⊢ ¬ ⊥
2	1	intnan 880	. 2 ⊢ ¬ ( ⊤ ∧ ⊥ )
3	2	bifal 1327	1 ⊢ (( ⊤ ∧ ⊥ ) ↔ ⊥ )

Syntax hints:   ↔ wb 176   ∧ wa 358   ⊤ wtru 1316   ⊥ wfal 1317

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 177  df-an 360  df-tru 1319  df-fal 1320

This theorem is referenced by:  trunanfal  1355