Theorem bj-nfs1 36758

Description: Shorter proof of nfs1 2496 (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 36757	. 2 ⊢ (∀𝑥Ⅎ𝑦𝜑 → Ⅎ𝑥[𝑦 / 𝑥]𝜑)
2		bj-nfs1.nf	. 2 ⊢ Ⅎ𝑦𝜑
3	1, 2	mpg 1795	1 ⊢ Ⅎ𝑥[𝑦 / 𝑥]𝜑

Syntax hints:  Ⅎwnf 1781  [wsb 2064

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1793  ax-4 1807  ax-5 1909  ax-6 1967  ax-7 2007  ax-10 2141  ax-12 2178  ax-13 2380

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 847  df-ex 1778  df-nf 1782  df-sb 2065

This theorem is referenced by: (None)