Theorem sb9 1264

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 1263	. 2 |- (A.x[x / y]ph -> A.y[y / x]ph)
2		sb9i 1263	. 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 954  [wsbc 1170

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 962  ax-gen 963  ax-8 964  ax-9 965  ax-10 966  ax-12 968  ax-4 973  ax-5o 975  ax-6o 978  ax-9o 1123  ax-10o 1140  ax-11o 1218

This theorem depends on definitions:  df-bi 147  df-or 224  df-an 225  df-ex 981  df-sb 1172

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