Theorem sb9 921

Description: Commutation of quantification and substitution variables.

Assertion

Ref	Expression
sb9	|- (A.x[x / y]ph <-> A.y[y / x]ph)

Proof of Theorem sb9

Step	Hyp	Ref	Expression
1		sb9i 920	. 2 |- (A.x[x / y]ph -> A.y[y / x]ph)
2		sb9i 920	. 2 |- (A.y[y / x]ph -> A.x[x / y]ph)
3	1, 2	impbi 139	1 |- (A.x[x / y]ph <-> A.y[y / x]ph)

Syntax hints:   <-> wb 127  A.wal 672  [wsb 852

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6  ax-4 673  ax-5 674  ax-6 675  ax-7 676  ax-gen 677  ax-8 798  ax-9 799  ax-10 800  ax-11 801  ax-12 802

This theorem depends on definitions:  df-bi 128  df-or 197  df-an 198  df-ex 679  df-sb 853

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