Theorem bj-sbf3 32826

Description: Substitution has no effect on a bound variabe (existential quantifier case); see sbf2 2382. (Contributed by BJ, 2-May-2019.)

Assertion

Ref	Expression
bj-sbf3	|- ( [ y / x ] E. x ph <-> E. x ph )

Proof of Theorem bj-sbf3

Step	Hyp	Ref	Expression
1		nfe1 2027	. 2 |- F/ x E. x ph
2	1	sbf 2380	1 |- ( [ y / x ] E. x ph <-> E. x ph )

Syntax hints:   <-> wb 196   E.wex 1704   [wsb 1880

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-10 2019  ax-12 2047  ax-13 2246

This theorem depends on definitions:  df-bi 197  df-an 386  df-ex 1705  df-nf 1710  df-sb 1881

This theorem is referenced by: (None)