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Theorem sbied 2151
Description: Conversion of implicit substitution to explicit substitution (deduction version of sbie 2149). (Contributed by NM, 30-Jun-1994.) (Revised by Mario Carneiro, 4-Oct-2016.) (Proof shortened by Wolf Lammen, 24-Jun-2018.)
Hypotheses
Ref Expression
sbied.1
sbied.2
sbied.3
Assertion
Ref Expression
sbied

Proof of Theorem sbied
StepHypRef Expression
1 sbied.1 . . . 4
21sbrim 2137 . . 3
3 sbied.2 . . . . 5
41, 3nfim1 1919 . . . 4
5 sbied.3 . . . . . 6
65com12 31 . . . . 5
76pm5.74d 247 . . . 4
84, 7sbie 2149 . . 3
92, 8bitr3i 251 . 2
109pm5.74ri 246 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  <->wb 184  F/wnf 1616  [wsb 1739
This theorem is referenced by:  sbiedv  2152  sbco2  2158  wl-equsb3  30004
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-12 1854  ax-13 1999
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-ex 1613  df-nf 1617  df-sb 1740
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