Theorem bj-sbf3 37277

Description: Substitution has no effect on a bound variable (existential quantifier case); see sbf2 2305. (Contributed by BJ, 2-May-2019.)

Assertion

Ref	Expression
bj-sbf3	⊢ ([𝑦 / 𝑥]∃𝑥𝜑 ↔ ∃𝑥𝜑)

Proof of Theorem bj-sbf3

Step	Hyp	Ref	Expression
1		nfe1 2183	. 2 ⊢ Ⅎ𝑥∃𝑥𝜑
2	1	sbf 2304	1 ⊢ ([𝑦 / 𝑥]∃𝑥𝜑 ↔ ∃𝑥𝜑)

Syntax hints:   ↔ wb 208  ∃wex 1798  [wsb 2089

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1814  ax-4 1828  ax-5 1929  ax-6 1986  ax-7 2027  ax-10 2174  ax-12 2211

This theorem depends on definitions:  df-bi 209  df-an 400  df-ex 1799  df-nf 1803  df-sb 2090

This theorem is referenced by: (None)