Theorem sbequ5 1190

Description: Substitution does not change an identical variable specifier.

Assertion

Ref	Expression
sbequ5	|- ([w / z]A.x x = y <-> A.x x = y)

Proof of Theorem sbequ5

Step	Hyp	Ref	Expression
1		hbae 1145	. 2 |- (A.x x = y -> A.zA.x x = y)
2	1	sbf 1186	1 |- ([w / z]A.x x = y <-> A.x x = y)

Syntax hints:   <-> wb 146  A.wal 954   = wceq 956  [wsbc 1170

This theorem is referenced by:  sbal 1347

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 962  ax-gen 963  ax-10 966  ax-12 968  ax-4 973  ax-5o 975  ax-6o 978  ax-9o 1123  ax-10o 1140

This theorem depends on definitions:  df-bi 147  df-or 224  df-an 225  df-ex 981  df-sb 1172

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