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Theorem bnj1154 29305
 Description: Property of . (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Assertion
Ref Expression
bnj1154
Distinct variable groups:   ,,   ,,   ,,

Proof of Theorem bnj1154
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 bnj658 29056 . 2
2 elisset 2958 . . . . 5
32bnj708 29061 . . . 4
4 df-fr 4533 . . . . . . . 8
54biimpi 187 . . . . . . 7
6519.21bi 1774 . . . . . 6
763impib 1151 . . . . 5
8 sseq1 3361 . . . . . . 7
9 neeq1 2606 . . . . . . 7
108, 93anbi23d 1257 . . . . . 6
11 raleq 2896 . . . . . . 7
1211rexeqbi1dv 2905 . . . . . 6
1310, 12imbi12d 312 . . . . 5
147, 13mpbii 203 . . . 4
153, 14bnj593 29050 . . 3
1615bnj937 29079 . 2
171, 16mpd 15 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wa 359   w3a 936  wal 1549  wex 1550   wceq 1652   wcel 1725   wne 2598  wral 2697  wrex 2698  cvv 2948   wss 3312  c0 3620   class class class wbr 4204   wfr 4530   w-bnj17 28987 This theorem is referenced by:  bnj1190  29314 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 2416 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 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ne 2600  df-ral 2702  df-rex 2703  df-v 2950  df-in 3319  df-ss 3326  df-fr 4533  df-bnj17 28988
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