Theorem bj-sbf4 32015

Description: Substitution has no effect on a bound variabe (non-freeness case); see sbf2 2370. (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 2018	. 2 ⊢ Ⅎ𝑥Ⅎ𝑥𝜑
2	1	sbf 2368	1 ⊢ ([𝑦 / 𝑥]Ⅎ𝑥𝜑 ↔ Ⅎ𝑥𝜑)

Syntax hints:   ↔ wb 195  Ⅎwnf 1699  [wsb 1867

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-10 2006  ax-12 2034  ax-13 2234

This theorem depends on definitions:  df-bi 196  df-or 384  df-an 385  df-tru 1478  df-ex 1696  df-nf 1701  df-sb 1868

This theorem is referenced by: (None)