Theorem eqsb3lem 2181

Description: Lemma for eqsb3 2182. (Contributed by Rodolfo Medina, 28-Apr-2010.) (Proof shortened by Andrew Salmon, 14-Jun-2011.)

Assertion

Ref	Expression
eqsb3lem	|- ( [ x / y ] y = A <-> x = A )

Distinct variable groups:   x, y   y, A

Allowed substitution hint:   A( x)

Proof of Theorem eqsb3lem

Step	Hyp	Ref	Expression
1		nfv 1461	. 2 |- F/ y x = A
2		eqeq1 2087	. 2 |- ( y = x -> ( y = A <-> x = A ) )
3	1, 2	sbie 1714	1 |- ( [ x / y ] y = A <-> x = A )

Syntax hints:   <-> wb 103   = wceq 1284   [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-4 1440  ax-17 1459  ax-i9 1463  ax-ial 1467  ax-ext 2063

This theorem depends on definitions:  df-bi 115  df-nf 1390  df-sb 1686  df-cleq 2074

This theorem is referenced by:  eqsb3  2182