Theorem bj-nfs1 37455

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 37454	. 2 ⊢ (∀𝑥Ⅎ𝑦𝜑 → Ⅎ𝑥[𝑦 / 𝑥]𝜑)
2		bj-nfs1.nf	. 2 ⊢ Ⅎ𝑦𝜑
3	1, 2	mpg 1826	1 ⊢ Ⅎ𝑥[𝑦 / 𝑥]𝜑

This proof depends on syntax axioms:  Ⅎwnf 1812  [wsb 2095

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1824  ax-4 1838  ax-5 1939  ax-6 1996  ax-7 2037  ax-10 2175  ax-12 2212  ax-13 2403

This proof depends on definitions:  df-bi 210  df-an 401  df-or 861  df-ex 1809  df-nf 1813  df-sb 2096

This theorem is used by: (None)