Theorem anabss4

Description: Absorption of antecedent into conjunction. (Contributed by NM, 20-Jul-1996)

	Ref	Expression
Hypothesis	anabss4.1	⊢ ( ( ( 𝜓 ∧ 𝜑 ) ∧ 𝜓 ) → 𝜒 )
Assertion	anabss4	⊢ ( ( 𝜑 ∧ 𝜓 ) → 𝜒 )

Proof

Step	Hyp	Ref	Expression
1		anabss4.1	⊢ ( ( ( 𝜓 ∧ 𝜑 ) ∧ 𝜓 ) → 𝜒 )
2	1	anabss1	⊢ ( ( 𝜓 ∧ 𝜑 ) → 𝜒 )
3	2	ancoms	⊢ ( ( 𝜑 ∧ 𝜓 ) → 𝜒 )