Theorem eqsb3lem 2191

Description: Lemma for eqsb3 2192. (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 1467	. 2 |- F/ y x = A
2		eqeq1 2095	. 2 |- ( y = x -> ( y = A <-> x = A ) )
3	1, 2	sbie 1722	1 |- ( [ x / y ] y = A <-> x = A )

Syntax hints:   <-> wb 104   = wceq 1290   [wsb 1693

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1382  ax-gen 1384  ax-ie1 1428  ax-ie2 1429  ax-4 1446  ax-17 1465  ax-i9 1469  ax-ial 1473  ax-ext 2071

This theorem depends on definitions:  df-bi 116  df-nf 1396  df-sb 1694  df-cleq 2082

This theorem is referenced by:  eqsb3  2192