Theorem nfs1f 2520

Description: If 𝑥 is not free in 𝜑, it is not free in [𝑦 / 𝑥]𝜑. (Contributed by Mario Carneiro, 11-Aug-2016.)

Hypothesis

Ref	Expression
nfs1f.1	⊢ Ⅎ𝑥𝜑

Assertion

Ref	Expression
nfs1f	⊢ Ⅎ𝑥[𝑦 / 𝑥]𝜑

Proof of Theorem nfs1f

Step	Hyp	Ref	Expression
1		nfs1f.1	. . 3 ⊢ Ⅎ𝑥𝜑
2	1	sbf 2517	. 2 ⊢ ([𝑦 / 𝑥]𝜑 ↔ 𝜑)
3	2, 1	nfxfr 1928	1 ⊢ Ⅎ𝑥[𝑦 / 𝑥]𝜑

Syntax hints:  Ⅎwnf 1857  [wsb 2046

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1871  ax-4 1886  ax-5 1988  ax-6 2054  ax-7 2090  ax-12 2196  ax-13 2391

This theorem depends on definitions:  df-bi 197  df-an 385  df-ex 1854  df-nf 1859  df-sb 2047

This theorem is referenced by: (None)