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Theorem sbabelOLD 2651
Description: Obsolete proof of sbabel 2650 as of 26-Dec-2019. (Contributed by NM, 27-Sep-2003.) (Revised by Mario Carneiro, 7-Oct-2016.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypothesis
Ref Expression
sbabel.1
Assertion
Ref Expression
sbabelOLD
Distinct variable groups:   ,   ,

Proof of Theorem sbabelOLD
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 sbex 2207 . . 3
2 sban 2140 . . . . 5
3 nfv 1707 . . . . . . . . . 10
43sbf 2121 . . . . . . . . 9
54sbrbis 2146 . . . . . . . 8
65sbalv 2208 . . . . . . 7
7 abeq2 2581 . . . . . . . 8
87sbbii 1746 . . . . . . 7
9 abeq2 2581 . . . . . . 7
106, 8, 93bitr4i 277 . . . . . 6
11 sbabel.1 . . . . . . . 8
1211nfcri 2612 . . . . . . 7
1312sbf 2121 . . . . . 6
1410, 13anbi12i 697 . . . . 5
152, 14bitri 249 . . . 4
1615exbii 1667 . . 3
171, 16bitri 249 . 2
18 df-clel 2452 . . 3
1918sbbii 1746 . 2
20 df-clel 2452 . 2
2117, 19, 203bitr4i 277 1
Colors of variables: wff setvar class
Syntax hints:  <->wb 184  /\wa 369  A.wal 1393  =wceq 1395  E.wex 1612  [wsb 1739  e.wcel 1818  {cab 2442  F/_wnfc 2605
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-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607
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