Theorem sbequ5 1188

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 1143	. 2 |- (A.x x = y -> A.zA.x x = y)
2	1	sbf 1184	1 |- ([w / z]A.x x = y <-> A.x x = y)

Syntax hints:   <-> wb 146  A.wal 952   = wceq 954  [wsbc 1168

This theorem is referenced by:  sbal 1345

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 960  ax-gen 961  ax-10 964  ax-12 966  ax-4 971  ax-5o 973  ax-6o 976  ax-9o 1121  ax-10o 1138

This theorem depends on definitions:  df-bi 147  df-or 224  df-an 225  df-ex 979  df-sb 1170

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