Theorem sb9i 2427

Description: Commutation of quantification and substitution variables. (Contributed by NM, 5-Aug-1993.) (Proof shortened by Wolf Lammen, 15-Jun-2019.)

Assertion

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

Proof of Theorem sb9i

Step	Hyp	Ref	Expression
1		sb9 2426	. 2 |- ( A. x [ x / y ] ph <-> A. y [ y / x ] ph )
2	1	biimpi 206	1 |- ( A. x [ x / y ] ph -> A. y [ y / x ] ph )

Syntax hints:   -> wi 4   A.wal 1481   [wsb 1880

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-10 2019  ax-11 2034  ax-12 2047  ax-13 2246

This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-tru 1486  df-ex 1705  df-nf 1710  df-sb 1881

This theorem is referenced by: (None)