Metamath Proof Explorer


Theorem com23

Description: Commutation of antecedents. Swap 2nd and 3rd. Deduction associated with com12 . (Contributed by NM, 27-Dec-1992) (Proof shortened by Wolf Lammen, 4-Aug-2012)

Ref Expression
Hypothesis com3.1 ⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → 𝜃 ) ) )
Assertion com23 ( 𝜑 → ( 𝜒 → ( 𝜓 → 𝜃 ) ) )

Proof

Step Hyp Ref Expression
1 com3.1 ⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → 𝜃 ) ) )
2 pm2.27 ⊢ ( 𝜒 → ( ( 𝜒 → 𝜃 ) → 𝜃 ) )
3 1 2 syl9 ⊢ ( 𝜑 → ( 𝜒 → ( 𝜓 → 𝜃 ) ) )