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Metamath Proof Explorer

Theorem imim1d

Description: Deduction adding nested consequents. Deduction associated with imim1 and imim1i . (Contributed by NM, 3-Apr-1994) (Proof shortened by Wolf Lammen, 12-Sep-2012)

		Ref	Expression
	Hypothesis	imim1d.1	⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) )
	Assertion	imim1d	⊢ ( 𝜑 → ( ( 𝜒 → 𝜃 ) → ( 𝜓 → 𝜃 ) ) )

Proof

Step	Hyp	Ref	Expression
1		imim1d.1	⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) )
2		idd	⊢ ( 𝜑 → ( 𝜃 → 𝜃 ) )
3	1 2	imim12d	⊢ ( 𝜑 → ( ( 𝜒 → 𝜃 ) → ( 𝜓 → 𝜃 ) ) )