Theorem mncply

Description: A monic polynomial is a polynomial. (Contributed by Stefan O'Rear, 5-Dec-2014)

	Ref	Expression
Assertion	mncply	⊢ ( 𝑃 ∈ ( Monic ‘ 𝑆 ) → 𝑃 ∈ ( Poly ‘ 𝑆 ) )

Proof

Step	Hyp	Ref	Expression
1		elmnc	⊢ ( 𝑃 ∈ ( Monic ‘ 𝑆 ) ↔ ( 𝑃 ∈ ( Poly ‘ 𝑆 ) ∧ ( ( coeff ‘ 𝑃 ) ‘ ( deg ‘ 𝑃 ) ) = 1 ) )
2	1	simplbi	⊢ ( 𝑃 ∈ ( Monic ‘ 𝑆 ) → 𝑃 ∈ ( Poly ‘ 𝑆 ) )