Metamath Proof Explorer


Theorem pm3.3

Description: Theorem *3.3 (Exp) of WhiteheadRussell p. 112. (Contributed by NM, 3-Jan-2005) (Proof shortened by Wolf Lammen, 24-Mar-2013)

Ref Expression
Assertion pm3.3 ( ( ( 𝜑𝜓 ) → 𝜒 ) → ( 𝜑 → ( 𝜓𝜒 ) ) )

Proof

Step Hyp Ref Expression
1 id ( ( ( 𝜑𝜓 ) → 𝜒 ) → ( ( 𝜑𝜓 ) → 𝜒 ) )
2 1 expd ( ( ( 𝜑𝜓 ) → 𝜒 ) → ( 𝜑 → ( 𝜓𝜒 ) ) )