Theorem sbequ5 2031

Description: Substitution does not change an identical variable specifier. (Contributed by NM, 5-Aug-1993.)

Assertion

Ref	Expression
sbequ5	⊢ ([w / z]∀x x = y ↔ ∀x x = y)

Proof of Theorem sbequ5

Step	Hyp	Ref	Expression
1		nfae 1954	. 2 ⊢ Ⅎz∀x x = y
2	1	sbf 2026	1 ⊢ ([w / z]∀x x = y ↔ ∀x x = y)

Syntax hints:   ↔ wb 176  ∀wal 1540  [wsb 1648

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925

This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649

This theorem is referenced by:  sbal  2127