Theorem bj-sbf4 33739

Description: Substitution has no effect on a bound variable (nonfreeness case); see sbf2 2237. (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 2126	. 2 ⊢ Ⅎ𝑥Ⅎ𝑥𝜑
2	1	sbf 2236	1 ⊢ ([𝑦 / 𝑥]Ⅎ𝑥𝜑 ↔ Ⅎ𝑥𝜑)

Syntax hints:   ↔ wb 207  Ⅎwnf 1769  [wsb 2044

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1781  ax-4 1795  ax-5 1892  ax-6 1951  ax-7 1996  ax-10 2114  ax-12 2143

This theorem depends on definitions:  df-bi 208  df-an 397  df-or 843  df-ex 1766  df-nf 1770  df-sb 2045

This theorem is referenced by: (None)