Theorem bj-sbf4 34158

Description: Substitution has no effect on a bound variable (nonfreeness case); see sbf2 2268. (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 2154	. 2 ⊢ Ⅎ𝑥Ⅎ𝑥𝜑
2	1	sbf 2267	1 ⊢ ([𝑦 / 𝑥]Ⅎ𝑥𝜑 ↔ Ⅎ𝑥𝜑)

Syntax hints:   ↔ wb 208  Ⅎwnf 1780  [wsb 2065

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1792  ax-4 1806  ax-5 1907  ax-6 1966  ax-7 2011  ax-10 2141  ax-12 2173

This theorem depends on definitions:  df-bi 209  df-an 399  df-or 844  df-ex 1777  df-nf 1781  df-sb 2066

This theorem is referenced by: (None)