Metamath Proof Explorer


Theorem expdimp

Description: A deduction version of exportation, followed by importation. (Contributed by NM, 6-Sep-2008)

Ref Expression
Hypothesis expdimp.1 ( 𝜑 → ( ( 𝜓𝜒 ) → 𝜃 ) )
Assertion expdimp ( ( 𝜑𝜓 ) → ( 𝜒𝜃 ) )

Proof

Step Hyp Ref Expression
1 expdimp.1 ( 𝜑 → ( ( 𝜓𝜒 ) → 𝜃 ) )
2 1 expd ( 𝜑 → ( 𝜓 → ( 𝜒𝜃 ) ) )
3 2 imp ( ( 𝜑𝜓 ) → ( 𝜒𝜃 ) )