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Theorem bj-2upleq 34057
 Description: Substitution property for (| , |). (Contributed by BJ, 6-Oct-2018.)
Assertion
Ref Expression
bj-2upleq (|, |) (|, |)

Proof of Theorem bj-2upleq
StepHypRef Expression
1 bj-1upleq 34044 . . 3 (||) (||)
2 bj-xtageq 34033 . . 3 tag tag
3 uneq12 3658 . . . 4 (||) (||) tag tag (||) tag (||) tag
43ex 434 . . 3 (||) (||) tag tag (||) tag (||) tag
51, 2, 4syl2im 38 . 2 (||) tag (||) tag
6 df-bj-2upl 34056 . . 3 (|, |) (||) tag
7 df-bj-2upl 34056 . . 3 (|, |) (||) tag
86, 7eqeq12i 2487 . 2 (|, |) (|, |) (||) tag (||) tag
95, 8syl6ibr 227 1 (|, |) (|, |)
 Colors of variables: wff setvar class Syntax hints:   wi 4   wceq 1379   cun 3479  csn 4033   cxp 5003  c1o 7135  tag bj-ctag 34019  (|bj-c1upl 34042  (|bj-c2uple 34055 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1601  ax-4 1612  ax-5 1680  ax-6 1719  ax-7 1739  ax-10 1786  ax-11 1791  ax-12 1803  ax-13 1968  ax-ext 2445 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1382  df-ex 1597  df-nf 1600  df-sb 1712  df-clab 2453  df-cleq 2459  df-clel 2462  df-nfc 2617  df-rex 2823  df-v 3120  df-un 3486  df-opab 4512  df-xp 5011  df-bj-sngl 34011  df-bj-tag 34020  df-bj-1upl 34043  df-bj-2upl 34056 This theorem is referenced by:  bj-2uplth  34066
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