Theorem sb9 1263

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 1262	. 2 |- (A.x[x / y]ph -> A.y[y / x]ph)
2		sb9i 1262	. 2 |- (A.y[y / x]ph -> A.x[x / y]ph)
3	1, 2	impbi 157	1 |- (A.x[x / y]ph <-> A.y[y / x]ph)

Syntax hints:   <-> wb 146  A.wal 953  [wsbc 1169

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 961  ax-gen 962  ax-8 963  ax-9 964  ax-10 965  ax-12 967  ax-4 972  ax-5o 974  ax-6o 977  ax-9o 1122  ax-10o 1139  ax-11o 1217

This theorem depends on definitions:  df-bi 147  df-or 224  df-an 225  df-ex 980  df-sb 1171

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