Theorem imim2d

Description: Deduction adding nested antecedents. Deduction associated with imim2 and imim2i . (Contributed by NM, 10-Jan-1993)

	Ref	Expression
Hypothesis	imim2d.1	⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) )
Assertion	imim2d	⊢ ( 𝜑 → ( ( 𝜃 → 𝜓 ) → ( 𝜃 → 𝜒 ) ) )

Proof

Step	Hyp	Ref	Expression
1		imim2d.1	⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) )
2	1	a1d	⊢ ( 𝜑 → ( 𝜃 → ( 𝜓 → 𝜒 ) ) )
3	2	a2d	⊢ ( 𝜑 → ( ( 𝜃 → 𝜓 ) → ( 𝜃 → 𝜒 ) ) )