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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.) (Proof modification is discouraged.) (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-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: (None)
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