Theorem bj-nfs1 37237

Description: Shorter proof of nfs1 2518 (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 37236	. 2 ⊢ (∀𝑥Ⅎ𝑦𝜑 → Ⅎ𝑥[𝑦 / 𝑥]𝜑)
2		bj-nfs1.nf	. 2 ⊢ Ⅎ𝑦𝜑
3	1, 2	mpg 1816	1 ⊢ Ⅎ𝑥[𝑦 / 𝑥]𝜑

Syntax hints:  Ⅎwnf 1802  [wsb 2089

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1814  ax-4 1828  ax-5 1929  ax-6 1986  ax-7 2027  ax-10 2174  ax-12 2211  ax-13 2402

This theorem depends on definitions:  df-bi 209  df-an 400  df-or 859  df-ex 1799  df-nf 1803  df-sb 2090

This theorem is referenced by: (None)