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Theorem bnj610 29345
 Description: Pass from equality ( ) to substitution ( ) without the distinct variable restriction (\$d ). (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Hypotheses
Ref Expression
bnj610.1
bnj610.2
bnj610.3
bnj610.4
Assertion
Ref Expression
bnj610
Distinct variable groups:   ,   ,   ,   ,   ,
Allowed substitution hints:   ()   ()   ()   ()

Proof of Theorem bnj610
StepHypRef Expression
1 vex 3090 . . . 4
2 bnj610.3 . . . 4
31, 2sbcie 3340 . . 3
43sbcbii 3361 . 2
5 sbcco 3328 . 2
6 bnj610.1 . . 3
7 bnj610.4 . . 3
86, 7sbcie 3340 . 2
94, 5, 83bitr3i 278 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 187   wceq 1437   wcel 1870  cvv 3087  wsbc 3305 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1665  ax-4 1678  ax-5 1751  ax-6 1797  ax-7 1841  ax-10 1889  ax-11 1894  ax-12 1907  ax-13 2055  ax-ext 2407 This theorem depends on definitions:  df-bi 188  df-or 371  df-an 372  df-3an 984  df-tru 1440  df-ex 1660  df-nf 1664  df-sb 1790  df-clab 2415  df-cleq 2421  df-clel 2424  df-v 3089  df-sbc 3306 This theorem is referenced by:  bnj611  29517  bnj1000  29540
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