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Theorem bnj1109 32942
 Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Hypotheses
Ref Expression
bnj1109.1
bnj1109.2
Assertion
Ref Expression
bnj1109

Proof of Theorem bnj1109
StepHypRef Expression
1 bnj1109.2 . . . . . . 7
21ex 434 . . . . . 6
32a1i 11 . . . . 5
43ax-gen 1601 . . . 4
5 bnj1109.1 . . . . 5
6 impexp 446 . . . . . 6
76exbii 1644 . . . . 5
85, 7mpbi 208 . . . 4
9 exintr 1678 . . . 4
104, 8, 9mp2 9 . . 3
11 exancom 1648 . . 3
1210, 11mpbi 208 . 2
13 df-ne 2664 . . . 4
1413imbi1i 325 . . 3
15 pm2.61 171 . . . 4
1615imp 429 . . 3
1714, 16sylan2b 475 . 2
1812, 17bnj101 32874 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wi 4   wa 369  wal 1377   wceq 1379  wex 1596   wne 2662 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1601  ax-4 1612 This theorem depends on definitions:  df-bi 185  df-an 371  df-ex 1597  df-ne 2664 This theorem is referenced by:  bnj1030  33140  bnj1128  33143  bnj1145  33146
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