Metamath Proof Explorer


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 ) ) )