Theorem bj-nfs1 37522

Description: Shorter proof of nfs1 2519 (three essential steps instead of four). (Contributed by BJ, 2-May-2019.) (Proof modification is discouraged.)

Hypothesis

Ref	Expression
bj-nfs1.nf	⊢ Ⅎ𝑦𝜑

Assertion

Ref	Expression
bj-nfs1	⊢ Ⅎ𝑥[𝑦 / 𝑥]𝜑

Proof of Theorem bj-nfs1

Step	Hyp	Ref	Expression
1		bj-nfs1t2 37521	. 2 ⊢ (∀𝑥Ⅎ𝑦𝜑 → Ⅎ𝑥[𝑦 / 𝑥]𝜑)
2		bj-nfs1.nf	. 2 ⊢ Ⅎ𝑦𝜑
3	1, 2	mpg 1830	1 ⊢ Ⅎ𝑥[𝑦 / 𝑥]𝜑

This proof depends on syntax axioms:  Ⅎwnf 1816  [wsb 2099

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1828  ax-4 1842  ax-5 1943  ax-6 2000  ax-7 2041  ax-10 2178  ax-12 2215  ax-13 2403

This proof depends on definitions:  df-bi 210  df-an 402  df-or 862  df-ex 1813  df-nf 1817  df-sb 2100

This theorem is used by: (None)