Theorem eqsb1lem 2290

Description: Lemma for eqsb1 2291. (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 1538	. 2 |- F/ x y = A
2		eqeq1 2194	. 2 |- ( x = y -> ( x = A <-> y = A ) )
3	1, 2	sbie 1801	1 |- ( [ y / x ] x = A <-> y = A )

Syntax hints:   <-> wb 105   = wceq 1363   [wsb 1772

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 1457  ax-gen 1459  ax-ie1 1503  ax-ie2 1504  ax-4 1520  ax-17 1536  ax-i9 1540  ax-ial 1544  ax-ext 2169

This theorem depends on definitions:  df-bi 117  df-nf 1471  df-sb 1773  df-cleq 2180

This theorem is referenced by:  eqsb1  2291