Theorem anabss3

Description: Absorption of antecedent into conjunction. (Contributed by NM, 20-Jul-1996) (Proof shortened by Wolf Lammen, 1-Jan-2013)

	Ref	Expression
Hypothesis	anabss3.1	⊢ ( ( ( 𝜑 ∧ 𝜓 ) ∧ 𝜓 ) → 𝜒 )
Assertion	anabss3	⊢ ( ( 𝜑 ∧ 𝜓 ) → 𝜒 )

Proof

Step	Hyp	Ref	Expression
1		anabss3.1	⊢ ( ( ( 𝜑 ∧ 𝜓 ) ∧ 𝜓 ) → 𝜒 )
2	1	anasss	⊢ ( ( 𝜑 ∧ ( 𝜓 ∧ 𝜓 ) ) → 𝜒 )
3	2	anabsan2	⊢ ( ( 𝜑 ∧ 𝜓 ) → 𝜒 )