Theorem sbid2v 2008

Description: An identity law for substitution. Used in proof of Theorem 9.7 of [Megill] p. 449 (p. 16 of the preprint). (Contributed by NM, 5-Aug-1993.)

Assertion

Ref	Expression
sbid2v	|- ( [ y / x ] [ x / y ] ph <-> ph )

Distinct variable group:   ph, x

Allowed substitution hint:   ph( y)

Proof of Theorem sbid2v

Step	Hyp	Ref	Expression
1		ax-17 1537	. 2 |- ( ph -> A. x ph )
2	1	sbid2h 1860	1 |- ( [ y / x ] [ x / y ] ph <-> ph )

Syntax hints:   <-> wb 105   [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-5 1458  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-8 1515  ax-11 1517  ax-4 1521  ax-17 1537  ax-i9 1541  ax-ial 1545

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

This theorem is referenced by:  bdph  15055