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Theorem spcimedv 2995
 Description: Restricted existential specialization, using implicit substitution. (Contributed by Mario Carneiro, 4-Jan-2017.)
Hypotheses
Ref Expression
spcimdv.1
spcimedv.2
Assertion
Ref Expression
spcimedv
Distinct variable groups:   ,   ,   ,
Allowed substitution hints:   ()   ()

Proof of Theorem spcimedv
StepHypRef Expression
1 spcimdv.1 . . . 4
2 spcimedv.2 . . . . 5
32con3d 127 . . . 4
41, 3spcimdv 2993 . . 3
54con2d 109 . 2
6 df-ex 1548 . 2
75, 6syl6ibr 219 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wa 359  wal 1546  wex 1547   wceq 1649   wcel 1721 This theorem is referenced by:  hashf1rn  11591 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1662  ax-8 1683  ax-6 1740  ax-7 1745  ax-11 1757  ax-12 1946  ax-ext 2385 This theorem depends on definitions:  df-bi 178  df-an 361  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-clab 2391  df-cleq 2397  df-clel 2400  df-nfc 2529  df-v 2918
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