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Theorem exsbOLD 2131
 Description: An equivalent expression for existence. Obsolete as of 19-Jun-2017. (Contributed by NM, 2-Feb-2005.) (New usage is discouraged.)
Assertion
Ref Expression
exsbOLD (xφyx(x = yφ))
Distinct variable groups:   x,y   φ,y
Allowed substitution hint:   φ(x)

Proof of Theorem exsbOLD
StepHypRef Expression
1 nfv 1619 . . 3 yφ
21sb8e 2093 . 2 (xφy[y / x]φ)
3 sb6 2099 . . 3 ([y / x]φx(x = yφ))
43exbii 1582 . 2 (y[y / x]φyx(x = yφ))
52, 4bitri 240 1 (xφyx(x = yφ))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ↔ wb 176  ∀wal 1540  ∃wex 1541   = wceq 1642  [wsb 1648 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 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: (None)
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