Theorem mpanl12

Description: An inference based on modus ponens. (Contributed by NM, 13-Jul-2005)

	Ref	Expression
Hypotheses	mpanl12.1	⊢ 𝜑
	mpanl12.2	⊢ 𝜓
	mpanl12.3	⊢ ( ( ( 𝜑 ∧ 𝜓 ) ∧ 𝜒 ) → 𝜃 )
Assertion	mpanl12	⊢ ( 𝜒 → 𝜃 )

Proof

Step	Hyp	Ref	Expression
1		mpanl12.1	⊢ 𝜑
2		mpanl12.2	⊢ 𝜓
3		mpanl12.3	⊢ ( ( ( 𝜑 ∧ 𝜓 ) ∧ 𝜒 ) → 𝜃 )
4	1 3	mpanl1	⊢ ( ( 𝜓 ∧ 𝜒 ) → 𝜃 )
5	2 4	mpan	⊢ ( 𝜒 → 𝜃 )