Metamath Proof Explorer

Theorem anabs7

Description: Absorption into embedded conjunct. (Contributed by NM, 20-Jul-1996) (Proof shortened by Wolf Lammen, 17-Nov-2013)

Ref Expression
Assertion anabs7 ( ( 𝜓 ∧ ( 𝜑 ∧ 𝜓 ) ) ↔ ( 𝜑 ∧ 𝜓 ) )

Proof

Step Hyp Ref Expression
1 simpr ⊢ ( ( 𝜑 ∧ 𝜓 ) → 𝜓 )
2 1 pm4.71ri ⊢ ( ( 𝜑 ∧ 𝜓 ) ↔ ( 𝜓 ∧ ( 𝜑 ∧ 𝜓 ) ) )
3 2 bicomi ⊢ ( ( 𝜓 ∧ ( 𝜑 ∧ 𝜓 ) ) ↔ ( 𝜑 ∧ 𝜓 ) )