Theorem mpanr12

Description: An inference based on modus ponens. (Contributed by NM, 24-Jul-2009)

	Ref	Expression
Hypotheses	mpanr12.1	⊢ 𝜓
	mpanr12.2	⊢ 𝜒
	mpanr12.3	⊢ ( ( 𝜑 ∧ ( 𝜓 ∧ 𝜒 ) ) → 𝜃 )
Assertion	mpanr12	⊢ ( 𝜑 → 𝜃 )

Proof

Step	Hyp	Ref	Expression
1		mpanr12.1	⊢ 𝜓
2		mpanr12.2	⊢ 𝜒
3		mpanr12.3	⊢ ( ( 𝜑 ∧ ( 𝜓 ∧ 𝜒 ) ) → 𝜃 )
4	1 3	mpanr1	⊢ ( ( 𝜑 ∧ 𝜒 ) → 𝜃 )
5	2 4	mpan2	⊢ ( 𝜑 → 𝜃 )