Theorem sb9i 1968

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 1967	. 2 |- ( A. x [ x / y ] ph <-> A. y [ y / x ] ph )
2	1	biimpi 119	1 |- ( A. x [ x / y ] ph -> A. y [ y / x ] ph )

Syntax hints:   -> wi 4   A.wal 1341   [wsb 1750

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 699  ax-5 1435  ax-7 1436  ax-gen 1437  ax-ie1 1481  ax-ie2 1482  ax-8 1492  ax-10 1493  ax-11 1494  ax-i12 1495  ax-bndl 1497  ax-4 1498  ax-17 1514  ax-i9 1518  ax-ial 1522  ax-i5r 1523

This theorem depends on definitions:  df-bi 116  df-nf 1449  df-sb 1751

This theorem is referenced by: (None)