Theorem eqsb3lem 2727

Description: Lemma for eqsb3 2728. (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 1843	. 2 |- F/ y x = A
2		eqeq1 2626	. 2 |- ( y = x -> ( y = A <-> x = A ) )
3	1, 2	sbie 2408	1 |- ( [ x / y ] y = A <-> x = A )

Syntax hints:   <-> wb 196   = wceq 1483   [wsb 1880

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-9 1999  ax-10 2019  ax-12 2047  ax-13 2246  ax-ext 2602

This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-ex 1705  df-nf 1710  df-sb 1881  df-cleq 2615

This theorem is referenced by:  eqsb3  2728