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Theorem bnj1234 29319
 Description: Technical lemma for bnj60 29368. This lemma may no longer be used or have become an indirect lemma of the theorem in question (i.e. a lemma of a lemma... of the theorem). (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Hypotheses
Ref Expression
bnj1234.2
bnj1234.3
bnj1234.4
bnj1234.5
Assertion
Ref Expression
bnj1234
Distinct variable groups:   ,,   ,,   ,   ,   ,,   ,,
Allowed substitution hints:   (,,,)   (,)   (,,,)   (,,,)   (,,,)   (,)   (,,)   (,,)

Proof of Theorem bnj1234
StepHypRef Expression
1 fneq1 5526 . . . . 5
2 fveq1 5719 . . . . . . 7
3 reseq1 5132 . . . . . . . . . 10
43opeq2d 3983 . . . . . . . . 9
5 bnj1234.2 . . . . . . . . 9
6 bnj1234.4 . . . . . . . . 9
74, 5, 63eqtr4g 2492 . . . . . . . 8
87fveq2d 5724 . . . . . . 7
92, 8eqeq12d 2449 . . . . . 6
109ralbidv 2717 . . . . 5
111, 10anbi12d 692 . . . 4
1211rexbidv 2718 . . 3
1312cbvabv 2554 . 2
14 bnj1234.3 . 2
15 bnj1234.5 . 2
1613, 14, 153eqtr4i 2465 1
 Colors of variables: wff set class Syntax hints:   wa 359   wceq 1652  cab 2421  wral 2697  wrex 2698  cop 3809   cres 4872   wfn 5441  cfv 5446   c-bnj14 28989 This theorem is referenced by:  bnj1245  29320  bnj1256  29321  bnj1259  29322  bnj1296  29327  bnj1311  29330 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-ral 2702  df-rex 2703  df-rab 2706  df-v 2950  df-dif 3315  df-un 3317  df-in 3319  df-ss 3326  df-nul 3621  df-if 3732  df-sn 3812  df-pr 3813  df-op 3815  df-uni 4008  df-br 4205  df-opab 4259  df-rel 4877  df-cnv 4878  df-co 4879  df-dm 4880  df-res 4882  df-iota 5410  df-fun 5448  df-fn 5449  df-fv 5454
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