Theorem falantru 1445

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 109	. 2 ⊢ ((⊥ ∧ ⊤) → ⊥)
2		falim 1409	. 2 ⊢ (⊥ → (⊥ ∧ ⊤))
3	1, 2	impbii 126	1 ⊢ ((⊥ ∧ ⊤) ↔ ⊥)

Syntax hints:   ∧ wa 104   ↔ wb 105  ⊤wtru 1396  ⊥wfal 1400

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-in1 617  ax-in2 618

This theorem depends on definitions:  df-bi 117  df-tru 1398  df-fal 1401

This theorem is referenced by:  trubifal  1458  falxortru  1463  falxorfal  1464