Theorem anabss5

Description: Absorption of antecedent into conjunction. (Contributed by NM, 10-May-1994) (Proof shortened by Wolf Lammen, 1-Jan-2013)

	Ref	Expression
Hypothesis	anabss5.1	⊢ ( ( 𝜑 ∧ ( 𝜑 ∧ 𝜓 ) ) → 𝜒 )
Assertion	anabss5	⊢ ( ( 𝜑 ∧ 𝜓 ) → 𝜒 )

Proof

Step	Hyp	Ref	Expression
1		anabss5.1	⊢ ( ( 𝜑 ∧ ( 𝜑 ∧ 𝜓 ) ) → 𝜒 )
2	1	anassrs	⊢ ( ( ( 𝜑 ∧ 𝜑 ) ∧ 𝜓 ) → 𝜒 )
3	2	anabsan	⊢ ( ( 𝜑 ∧ 𝜓 ) → 𝜒 )