Metamath Proof Explorer


Theorem 3coml

Description: Commutation in antecedent. Rotate left. (Contributed by NM, 28-Jan-1996)

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

Proof

Step Hyp Ref Expression
1 3exp.1 ⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) → 𝜃 )
2 1 3com23 ⊢ ( ( 𝜑 ∧ 𝜒 ∧ 𝜓 ) → 𝜃 )
3 2 3com13 ⊢ ( ( 𝜓 ∧ 𝜒 ∧ 𝜑 ) → 𝜃 )