Theorem anabsi5

Description: Absorption of antecedent into conjunction. (Contributed by NM, 11-Jun-1995) (Proof shortened by Wolf Lammen, 18-Nov-2013)

	Ref	Expression
Hypothesis	anabsi5.1	⊢ ( 𝜑 → ( ( 𝜑 ∧ 𝜓 ) → 𝜒 ) )
Assertion	anabsi5	⊢ ( ( 𝜑 ∧ 𝜓 ) → 𝜒 )

Proof

Step	Hyp	Ref	Expression
1		anabsi5.1	⊢ ( 𝜑 → ( ( 𝜑 ∧ 𝜓 ) → 𝜒 ) )
2		simpl	⊢ ( ( 𝜑 ∧ 𝜓 ) → 𝜑 )
3	2 1	mpcom	⊢ ( ( 𝜑 ∧ 𝜓 ) → 𝜒 )