Theorem sbequ5 898

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		eq5 824	. 2 |- (A.x x = y -> A.zA.x x = y)
2	1	sbf 870	1 |- ([w / z]A.x x = y <-> A.x x = y)

Syntax hints:   <-> wb 127  A.wal 672   = weq 797  [wsb 852

This theorem is referenced by:  sbal 997

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6  ax-4 673  ax-5 674  ax-6 675  ax-7 676  ax-gen 677  ax-8 798  ax-9 799  ax-10 800  ax-12 802

This theorem depends on definitions:  df-bi 128  df-or 197  df-an 198  df-ex 679  df-sb 853

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