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Theorem sbied 2036
 Description: Conversion of implicit substitution to explicit substitution (deduction version of sbie 2038). (Contributed by NM, 30-Jun-1994.) (Revised by Mario Carneiro, 4-Oct-2016.)
Hypotheses
Ref Expression
sbied.1
sbied.2
sbied.3
Assertion
Ref Expression
sbied

Proof of Theorem sbied
StepHypRef Expression
1 sb1 1651 . . . 4
2 sbied.1 . . . . 5
3 sbied.3 . . . . . . 7
4 bi1 178 . . . . . . 7
53, 4syl6 29 . . . . . 6
65imp3a 420 . . . . 5
72, 6eximd 1770 . . . 4
81, 7syl5 28 . . 3
9 sbied.2 . . . 4
10919.9d 1782 . . 3
118, 10syld 40 . 2
129nfrd 1763 . . 3
13 bi2 189 . . . . . . 7
143, 13syl6 29 . . . . . 6
1514com23 72 . . . . 5
162, 15alimd 1764 . . . 4
17 sb2 2023 . . . 4
1816, 17syl6 29 . . 3
1912, 18syld 40 . 2
2011, 19impbid 183 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 176   wa 358  wal 1540  wex 1541  wnf 1544  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:  sbiedv  2037  sbie  2038  dvelimdf  2082  sbco2  2086
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