Theorem bj-sbf4 35023

Description: Substitution has no effect on a bound variable (nonfreeness case); see sbf2 2264. (Contributed by BJ, 2-May-2019.)

Assertion

Ref	Expression
bj-sbf4	⊢ ([𝑦 / 𝑥]Ⅎ𝑥𝜑 ↔ Ⅎ𝑥𝜑)

Proof of Theorem bj-sbf4

Step	Hyp	Ref	Expression
1		nfnf1 2151	. 2 ⊢ Ⅎ𝑥Ⅎ𝑥𝜑
2	1	sbf 2263	1 ⊢ ([𝑦 / 𝑥]Ⅎ𝑥𝜑 ↔ Ⅎ𝑥𝜑)

Syntax hints:   ↔ wb 205  Ⅎwnf 1786  [wsb 2067

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1913  ax-6 1971  ax-7 2011  ax-10 2137  ax-12 2171

This theorem depends on definitions:  df-bi 206  df-an 397  df-or 845  df-ex 1783  df-nf 1787  df-sb 2068

This theorem is referenced by: (None)