Metamath Proof Explorer


Theorem expcom

Description: Exportation inference with commuted antecedents. (Contributed by NM, 25-May-2005)

Ref Expression
Hypothesis ex.1 ( ( 𝜑𝜓 ) → 𝜒 )
Assertion expcom ( 𝜓 → ( 𝜑𝜒 ) )

Proof

Step Hyp Ref Expression
1 ex.1 ( ( 𝜑𝜓 ) → 𝜒 )
2 1 ex ( 𝜑 → ( 𝜓𝜒 ) )
3 2 com12 ( 𝜓 → ( 𝜑𝜒 ) )