Theorem sb9i 1996

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 1995	. 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 1362   [wsb 1773

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 710  ax-5 1458  ax-7 1459  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-8 1515  ax-10 1516  ax-11 1517  ax-i12 1518  ax-bndl 1520  ax-4 1521  ax-17 1537  ax-i9 1541  ax-ial 1545  ax-i5r 1546

This theorem depends on definitions:  df-bi 117  df-nf 1472  df-sb 1774

This theorem is referenced by: (None)