Theorem falantru 1334

Description: A ∧ identity. (Contributed by David A. Wheeler, 23-Feb-2018.)

Assertion

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

Proof of Theorem falantru

Step	Hyp	Ref	Expression
1		simpl 107	. 2 ⊢ ((⊥ ∧ ⊤) → ⊥)
2		falim 1298	. 2 ⊢ (⊥ → (⊥ ∧ ⊤))
3	1, 2	impbii 124	1 ⊢ ((⊥ ∧ ⊤) ↔ ⊥)

Syntax hints:   ∧ wa 102   ↔ wb 103  ⊤wtru 1285  ⊥wfal 1289

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-in1 576  ax-in2 577

This theorem depends on definitions:  df-bi 115  df-tru 1287  df-fal 1290

This theorem is referenced by:  trubifal  1347  falxortru  1352  falxorfal  1353