Metamath Proof Explorer


Theorem 3com23

Description: Commutation in antecedent. Swap 2nd and 3rd. (Contributed by NM, 28-Jan-1996) (Proof shortened by Wolf Lammen, 9-Apr-2022)

Ref Expression
Hypothesis 3exp.1 ⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) → 𝜃 )
Assertion 3com23 ( ( 𝜑 ∧ 𝜒 ∧ 𝜓 ) → 𝜃 )

Proof

Step Hyp Ref Expression
1 3exp.1 ⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) → 𝜃 )
2 1 3comr ⊢ ( ( 𝜒 ∧ 𝜑 ∧ 𝜓 ) → 𝜃 )
3 2 3com12 ⊢ ( ( 𝜑 ∧ 𝜒 ∧ 𝜓 ) → 𝜃 )