Theorem impancom

Description: Mixed importation/commutation inference. (Contributed by NM, 22-Jun-2013)

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

Proof

Step	Hyp	Ref	Expression
1		impancom.1	⊢ ( ( 𝜑 ∧ 𝜓 ) → ( 𝜒 → 𝜃 ) )
2	1	ex	⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → 𝜃 ) ) )
3	2	com23	⊢ ( 𝜑 → ( 𝜒 → ( 𝜓 → 𝜃 ) ) )
4	3	imp	⊢ ( ( 𝜑 ∧ 𝜒 ) → ( 𝜓 → 𝜃 ) )