Theorem sb9i 2033

Description: Commutation of quantification and substitution variables. (Contributed by NM, 5-Aug-1993.) (Proof rewritten by Jim Kingdon, 23-Mar-2018.)

Assertion

Ref	Expression
sb9i	|- ( A. x [ x / y ] ph -> A. y [ y / x ] ph )

Proof of Theorem sb9i

Step	Hyp	Ref	Expression
1		sb9 2032	. 2 |- ( A. x [ x / y ] ph <-> A. y [ y / x ] ph )
2	1	biimpi 120	1 |- ( A. x [ x / y ] ph -> A. y [ y / x ] ph )

Syntax hints:   -> wi 4   A.wal 1395   [wsb 1810

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 716  ax-5 1495  ax-7 1496  ax-gen 1497  ax-ie1 1541  ax-ie2 1542  ax-8 1552  ax-10 1553  ax-11 1554  ax-i12 1555  ax-bndl 1557  ax-4 1558  ax-17 1574  ax-i9 1578  ax-ial 1582  ax-i5r 1583

This theorem depends on definitions:  df-bi 117  df-nf 1509  df-sb 1811

This theorem is referenced by: (None)