Theorem eqsb3lem 2243

Description: Lemma for eqsb3 2244. (Contributed by Rodolfo Medina, 28-Apr-2010.) (Proof shortened by Andrew Salmon, 14-Jun-2011.)

Assertion

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

Distinct variable groups:   x, y   x, A

Allowed substitution hint:   A( y)

Proof of Theorem eqsb3lem

Step	Hyp	Ref	Expression
1		nfv 1509	. 2 |- F/ x y = A
2		eqeq1 2147	. 2 |- ( x = y -> ( x = A <-> y = A ) )
3	1, 2	sbie 1765	1 |- ( [ y / x ] x = A <-> y = A )

Syntax hints:   <-> wb 104   = wceq 1332   [wsb 1736

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1424  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-4 1488  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-ext 2122

This theorem depends on definitions:  df-bi 116  df-nf 1438  df-sb 1737  df-cleq 2133

This theorem is referenced by:  eqsb3  2244