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Metamath Proof Explorer

Theorem anabs5

Description: Absorption into embedded conjunct. (Contributed by NM, 20-Jul-1996) (Proof shortened by Wolf Lammen, 9-Dec-2012)

Ref Expression
Assertion anabs5 ⊢ φ ∧ φ ∧ ψ ↔ φ ∧ ψ

Proof

Step Hyp Ref Expression
1 ibar ⊢ φ → ψ ↔ φ ∧ ψ
2 1 bicomd ⊢ φ → φ ∧ ψ ↔ ψ
3 2 pm5.32i ⊢ φ ∧ φ ∧ ψ ↔ φ ∧ ψ