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Theorem bnj1109 29219
 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 425 . . . . . 6
32a1i 11 . . . . 5
43ax-gen 1556 . . . 4
5 bnj1109.1 . . . . 5
6 impexp 435 . . . . . 6
76exbii 1593 . . . . 5
85, 7mpbi 201 . . . 4
9 exintr 1625 . . . 4
104, 8, 9mp2 9 . . 3
11 exancom 1597 . . 3
1210, 11mpbi 201 . 2
13 df-ne 2603 . . . 4
1413imbi1i 317 . . 3
15 pm2.61 166 . . . 4
1615imp 420 . . 3
1714, 16sylan2b 463 . 2
1812, 17bnj101 29150 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wa 360  wal 1550  wex 1551   wceq 1653   wne 2601 This theorem is referenced by:  bnj1030  29418  bnj1128  29421  bnj1145  29424 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567 This theorem depends on definitions:  df-bi 179  df-an 362  df-ex 1552  df-ne 2603
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