Theorem mpg

Description: Modus ponens combined with generalization. (Contributed by NM, 24-May-1994)

	Ref	Expression
Hypotheses	mpg.1	⊢ ( ∀ 𝑥 𝜑 → 𝜓 )
	mpg.2	⊢ 𝜑
Assertion	mpg	⊢ 𝜓

Proof

Step	Hyp	Ref	Expression
1		mpg.1	⊢ ( ∀ 𝑥 𝜑 → 𝜓 )
2		mpg.2	⊢ 𝜑
3	2	ax-gen	⊢ ∀ 𝑥 𝜑
4	3 1	ax-mp	⊢ 𝜓