Theorem equsb3lem 2431

Description: Lemma for equsb3 2432. (Contributed by Raph Levien and FL, 4-Dec-2005.) (Proof shortened by Andrew Salmon, 14-Jun-2011.)

Assertion

Ref	Expression
equsb3lem	|- ( [ x / y ] y = z <-> x = z )

Distinct variable groups:   y, z   x, y

Proof of Theorem equsb3lem

Step	Hyp	Ref	Expression
1		nfv 1843	. 2 |- F/ y x = z
2		equequ1 1952	. 2 |- ( y = x -> ( y = z <-> x = z ) )
3	1, 2	sbie 2408	1 |- ( [ x / y ] y = z <-> x = z )

Syntax hints:   <-> wb 196   [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-10 2019  ax-12 2047  ax-13 2246

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

This theorem is referenced by:  equsb3  2432  equsb3ALT  2433