Metamath Proof Explorer

Theorem anandi3r

Description: Distribution of triple conjunction over conjunction. (Contributed by David A. Wheeler, 4-Nov-2018)

Ref Expression
Assertion anandi3r ⊢ φ ∧ ψ ∧ χ ↔ φ ∧ ψ ∧ χ ∧ ψ

Proof

Step Hyp Ref Expression
1 3anan32 ⊢ φ ∧ ψ ∧ χ ↔ φ ∧ χ ∧ ψ
2 anandir ⊢ φ ∧ χ ∧ ψ ↔ φ ∧ ψ ∧ χ ∧ ψ
3 1 2 bitri ⊢ φ ∧ ψ ∧ χ ↔ φ ∧ ψ ∧ χ ∧ ψ