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Theorem joinval2lem 15764
 Description: Lemma for joinval2 15765 and joineu 15766. (Contributed by NM, 12-Sep-2018.) TODO: combine this through joineu into joinlem?
Hypotheses
Ref Expression
joinval2.b
joinval2.l
joinval2.j
joinval2.k
joinval2.x
joinval2.y
Assertion
Ref Expression
joinval2lem
Distinct variable groups:   ,,   , ,   ,,,   ,   ,,,   ,,,
Allowed substitution hints:   (,,)   ()   ()   (,)   (,,)

Proof of Theorem joinval2lem
StepHypRef Expression
1 breq1 4459 . . 3
2 breq1 4459 . . 3
31, 2ralprg 4081 . 2
4 breq1 4459 . . . . 5
5 breq1 4459 . . . . 5
64, 5ralprg 4081 . . . 4
76imbi1d 317 . . 3
87ralbidv 2896 . 2
93, 8anbi12d 710 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 184   wa 369   wceq 1395   wcel 1819  wral 2807  cpr 4034   class class class wbr 4456  cfv 5594  cbs 14643  cple 14718  cjn 15699 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1619  ax-4 1632  ax-5 1705  ax-6 1748  ax-7 1791  ax-10 1838  ax-11 1843  ax-12 1855  ax-13 2000  ax-ext 2435 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1398  df-ex 1614  df-nf 1618  df-sb 1741  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ral 2812  df-rab 2816  df-v 3111  df-sbc 3328  df-dif 3474  df-un 3476  df-in 3478  df-ss 3485  df-nul 3794  df-if 3945  df-sn 4033  df-pr 4035  df-op 4039  df-br 4457 This theorem is referenced by:  joinval2  15765  joineu  15766
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