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Theorem sbied 1989
 Description: Conversion of implicit substitution to explicit substitution (deduction version of sbie 1991). (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 1641 . . . 4
2 sbied.1 . . . . 5
3 sbied.3 . . . . . . 7
4 bi1 178 . . . . . . 7
53, 4syl6 29 . . . . . 6
65imp3a 420 . . . . 5
72, 6eximd 1762 . . . 4
81, 7syl5 28 . . 3
9 sbied.2 . . . 4
10919.9d 1796 . . 3
118, 10syld 40 . 2
129nfrd 1755 . . 3
13 bi2 189 . . . . . . 7
143, 13syl6 29 . . . . . 6
1514com23 72 . . . . 5
162, 15alimd 1756 . . . 4
17 sb2 1976 . . . 4
1816, 17syl6 29 . . 3
1912, 18syld 40 . 2
2011, 19impbid 183 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 176   wa 358  wal 1530  wex 1531  wnf 1534  wsb 1638 This theorem is referenced by:  sbiedv  1990  sbie  1991  dvelimdf  2035  sbco2  2039  prtlem5  26825 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878 This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1532  df-nf 1535  df-sb 1639
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