Theorem cbvrexsv 1964

Description: Change bound variable by using a substitution.

Assertion

Ref	Expression
cbvrexsv	|- (E.x e. A ph <-> E.y e. A [y / x]ph)

Distinct variable groups:   x,y,A   ph,y

Proof of Theorem cbvrexsv

Step	Hyp	Ref	Expression
1		ax-17 969	. 2 |- (ph -> A.yph)
2		hbs1 1330	. 2 |- ([y / x]ph -> A.x[y / x]ph)
3		sbequ12 1179	. 2 |- (x = y -> (ph <-> [y / x]ph))
4	1, 2, 3	cbvrex 1795	1 |- (E.x e. A ph <-> E.y e. A [y / x]ph)

Syntax hints:   <-> wb 146  [wsbc 1168  E.wrex 1643

This theorem is referenced by:  ac6sf 4740

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 960  ax-gen 961  ax-8 962  ax-10 964  ax-12 966  ax-17 969  ax-4 971  ax-5o 973  ax-6o 976  ax-9o 1121  ax-10o 1138  ax-16 1208  ax-11o 1216  ax-ext 1457

This theorem depends on definitions:  df-bi 147  df-an 225  df-ex 979  df-sb 1170  df-cleq 1467  df-clel 1470  df-rex 1647

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