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Theorem bnj610 29115
 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 2959 . . . 4
2 bnj610.3 . . . 4
31, 2sbcie 3195 . . 3
43sbcbii 3216 . 2
5 sbcco 3183 . 2
6 bnj610.1 . . 3
7 bnj610.4 . . 3
86, 7sbcie 3195 . 2
94, 5, 83bitr3i 267 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wceq 1652   wcel 1725  cvv 2956  wsbc 3161 This theorem is referenced by:  bnj611  29289  bnj1000  29312 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-v 2958  df-sbc 3162
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