Theorem cbvmow 2096

Description: Rule used to change bound variables, using implicit substitution. Version of cbvmo 2095 with a disjoint variable condition. (Contributed by NM, 9-Mar-1995.) (Revised by GG, 23-May-2024.)

Hypotheses

Ref	Expression
cbvmow.1	|- F/ y ph
cbvmow.2	|- F/ x ps
cbvmow.3	|- ( x = y -> ( ph <-> ps ) )

Assertion

Ref	Expression
cbvmow	|- ( E* x ph <-> E* y ps )

Distinct variable group:   x, y

Allowed substitution hints:   ph( x, y)   ps( x, y)

Proof of Theorem cbvmow

Step	Hyp	Ref	Expression
1		cbvmow.1	. 2 |- F/ y ph
2		cbvmow.2	. 2 |- F/ x ps
3		cbvmow.3	. 2 |- ( x = y -> ( ph <-> ps ) )
4	1, 2, 3	cbvmo 2095	1 |- ( E* x ph <-> E* y ps )

Syntax hints:   -> wi 4   <-> wb 105   F/wnf 1484   E*wmo 2056

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 711  ax-5 1471  ax-7 1472  ax-gen 1473  ax-ie1 1517  ax-ie2 1518  ax-8 1528  ax-10 1529  ax-11 1530  ax-i12 1531  ax-bndl 1533  ax-4 1534  ax-17 1550  ax-i9 1554  ax-ial 1558  ax-i5r 1559

This theorem depends on definitions:  df-bi 117  df-tru 1376  df-nf 1485  df-sb 1787  df-eu 2058  df-mo 2059

This theorem is referenced by:  cbvrmow  2691