Theorem eqsb1lem 2341

Description: Lemma for eqsb1 2342. (Contributed by Rodolfo Medina, 28-Apr-2010.) (Proof shortened by Andrew Salmon, 14-Jun-2011.)

Assertion

Ref	Expression
eqsb1lem	|- ( [ y / x ] x = A <-> y = A )

Distinct variable groups:   x, y   x, A

Allowed substitution hint:   A( y)

Proof of Theorem eqsb1lem

Step	Hyp	Ref	Expression
1		nfv 1581	. 2 |- F/ x y = A
2		eqeq1 2245	. 2 |- ( x = y -> ( x = A <-> y = A ) )
3	1, 2	sbie 1844	1 |- ( [ y / x ] x = A <-> y = A )

Syntax hints:   <-> wb 105   = wceq 1402   [wsb 1815

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 1500  ax-gen 1502  ax-ie1 1546  ax-ie2 1547  ax-4 1563  ax-17 1579  ax-i9 1583  ax-ial 1587  ax-ext 2220

This theorem depends on definitions:  df-bi 117  df-nf 1514  df-sb 1816  df-cleq 2231

This theorem is referenced by:  eqsb1  2342