Theorem falantru 1294

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 102	. 2 ⊢ ((⊥ ∧ ⊤) → ⊥)
2		falim 1257	. 2 ⊢ (⊥ → (⊥ ∧ ⊤))
3	1, 2	impbii 117	1 ⊢ ((⊥ ∧ ⊤) ↔ ⊥)

Syntax hints:   ∧ wa 97   ↔ wb 98  ⊤wtru 1244  ⊥wfal 1248

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in1 544  ax-in2 545

This theorem depends on definitions:  df-bi 110  df-tru 1246  df-fal 1249

This theorem is referenced by:  trubifal  1307  falxortru  1312  falxorfal  1313