Metamath Proof Explorer


Theorem expr

Description: Export a wff from a right conjunct. (Contributed by Jeff Hankins, 30-Aug-2009)

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

Proof

Step Hyp Ref Expression
1 expr.1 ⊢ ( ( 𝜑 ∧ ( 𝜓 ∧ 𝜒 ) ) → 𝜃 )
2 1 exp32 ⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → 𝜃 ) ) )
3 2 imp ⊢ ( ( 𝜑 ∧ 𝜓 ) → ( 𝜒 → 𝜃 ) )