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Theorem bnj89 28820
 Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Hypothesis
Ref Expression
bnj89.1
Assertion
Ref Expression
bnj89
Distinct variable groups:   ,   ,
Allowed substitution hints:   (,)   ()

Proof of Theorem bnj89
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 bnj89.1 . . . 4
2 sbcexg 3043 . . . 4
31, 2ax-mp 8 . . 3
4 sbcalg 3041 . . . . 5
51, 4ax-mp 8 . . . 4
65exbii 1571 . . 3
7 sbcbig 3039 . . . . . . 7
81, 7ax-mp 8 . . . . . 6
9 sbcg 3058 . . . . . . . 8
101, 9ax-mp 8 . . . . . . 7
1110bibi2i 304 . . . . . 6
128, 11bitri 240 . . . . 5
1312albii 1555 . . . 4
1413exbii 1571 . . 3
153, 6, 143bitri 262 . 2
16 df-eu 2149 . . . 4
1716sbcbiiOLD 3049 . . 3
181, 17ax-mp 8 . 2
19 df-eu 2149 . 2
2015, 18, 193bitr4i 268 1
 Colors of variables: wff set class Syntax hints:   wb 176  wal 1529  wex 1530   wceq 1625   wcel 1686  weu 2145  cvv 2790  wsbc 2993 This theorem is referenced by:  bnj130  28979  bnj207  28986 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1535  ax-5 1546  ax-17 1605  ax-9 1637  ax-8 1645  ax-6 1705  ax-7 1710  ax-11 1717  ax-12 1868  ax-ext 2266 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1531  df-nf 1534  df-sb 1632  df-eu 2149  df-clab 2272  df-cleq 2278  df-clel 2281  df-nfc 2410  df-v 2792  df-sbc 2994
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