Theorem falantru 1393

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 108	. 2 ⊢ ((⊥ ∧ ⊤) → ⊥)
2		falim 1357	. 2 ⊢ (⊥ → (⊥ ∧ ⊤))
3	1, 2	impbii 125	1 ⊢ ((⊥ ∧ ⊤) ↔ ⊥)

Syntax hints:   ∧ wa 103   ↔ wb 104  ⊤wtru 1344  ⊥wfal 1348

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 604  ax-in2 605

This theorem depends on definitions:  df-bi 116  df-tru 1346  df-fal 1349

This theorem is referenced by:  trubifal  1406  falxortru  1411  falxorfal  1412