Theorem bj-nfs1

Description: Shorter proof of nfs1 (three essential steps instead of four). (Contributed by BJ, 2-May-2019) (Proof modification is discouraged.)

	Ref	Expression
Hypothesis	bj-nfs1.nf	⊢ Ⅎ 𝑦 𝜑
Assertion	bj-nfs1	⊢ Ⅎ 𝑥 [ 𝑦 / 𝑥 ] 𝜑

Proof

Step	Hyp	Ref	Expression
1		bj-nfs1.nf	⊢ Ⅎ 𝑦 𝜑
2		bj-nfs1t2	⊢ ( ∀ 𝑥 Ⅎ 𝑦 𝜑 → Ⅎ 𝑥 [ 𝑦 / 𝑥 ] 𝜑 )
3	2 1	mpg	⊢ Ⅎ 𝑥 [ 𝑦 / 𝑥 ] 𝜑