Theorem sb9 2095

Description: Commutation of quantification and substitution variables. (Contributed by NM, 5-Aug-1993.)

Assertion

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

Proof of Theorem sb9

Step	Hyp	Ref	Expression
1		sb9i 2094	. 2 |- (A.x[x / y]ph -> A.y[y / x]ph)
2		sb9i 2094	. 2 |- (A.y[y / x]ph -> A.x[x / y]ph)
3	1, 2	impbii 180	1 |- (A.x[x / y]ph <-> A.y[y / x]ph)

Syntax hints:   <-> wb 176  A.wal 1540  [wsb 1648

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925

This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649

This theorem is referenced by: (None)