Theorem sbid2v 1913

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 1459	. 2 |- ( ph -> A. x ph )
2	1	sbid2h 1770	1 |- ( [ y / x ] [ x / y ] ph <-> ph )

Syntax hints:   <-> wb 103   [wsb 1685

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1376  ax-gen 1378  ax-ie1 1422  ax-ie2 1423  ax-8 1435  ax-11 1437  ax-4 1440  ax-17 1459  ax-i9 1463  ax-ial 1467

This theorem depends on definitions:  df-bi 115  df-sb 1686

This theorem is referenced by:  bdph  10641