Theorem mpan2

Description: An inference based on modus ponens. (Contributed by NM, 16-Sep-1993) (Proof shortened by Wolf Lammen, 19-Nov-2012)

	Ref	Expression
Hypotheses	mpan2.1	⊢ 𝜓
	mpan2.2	⊢ ( ( 𝜑 ∧ 𝜓 ) → 𝜒 )
Assertion	mpan2	⊢ ( 𝜑 → 𝜒 )

Proof

Step	Hyp	Ref	Expression
1		mpan2.1	⊢ 𝜓
2		mpan2.2	⊢ ( ( 𝜑 ∧ 𝜓 ) → 𝜒 )
3	1	a1i	⊢ ( 𝜑 → 𝜓 )
4	3 2	mpdan	⊢ ( 𝜑 → 𝜒 )