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Theorem bj-1upln0 31603
Description: A monuple is nonempty. (Contributed by BJ, 6-Apr-2019.)
Assertion
Ref Expression
bj-1upln0  |- (| A|)  =/=  (/)

Proof of Theorem bj-1upln0
StepHypRef Expression
1 df-bj-1upl 31592 . 2  |- (| A|)  =  ( { (/) }  X. tag  A
)
2 0nep0 4574 . . . 4  |-  (/)  =/=  { (/)
}
32necomi 2678 . . 3  |-  { (/) }  =/=  (/)
4 bj-tagn0 31573 . . 3  |- tag  A  =/=  (/)
5 xpnz 5256 . . . 4  |-  ( ( { (/) }  =/=  (/)  /\ tag  A  =/=  (/) )  <->  ( { (/)
}  X. tag  A )  =/=  (/) )
65biimpi 198 . . 3  |-  ( ( { (/) }  =/=  (/)  /\ tag  A  =/=  (/) )  ->  ( { (/) }  X. tag  A
)  =/=  (/) )
73, 4, 6mp2an 678 . 2  |-  ( {
(/) }  X. tag  A )  =/=  (/)
81, 7eqnetri 2694 1  |- (| A|)  =/=  (/)
Colors of variables: wff setvar class
Syntax hints:    /\ wa 371    =/= wne 2622   (/)c0 3731   {csn 3968    X. cxp 4832  tag bj-ctag 31568  (|bj-c1upl 31591
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1669  ax-4 1682  ax-5 1758  ax-6 1805  ax-7 1851  ax-9 1896  ax-10 1915  ax-11 1920  ax-12 1933  ax-13 2091  ax-ext 2431  ax-sep 4525  ax-nul 4534  ax-pr 4639
This theorem depends on definitions:  df-bi 189  df-or 372  df-an 373  df-3an 987  df-tru 1447  df-ex 1664  df-nf 1668  df-sb 1798  df-eu 2303  df-mo 2304  df-clab 2438  df-cleq 2444  df-clel 2447  df-nfc 2581  df-ne 2624  df-ral 2742  df-rex 2743  df-rab 2746  df-v 3047  df-dif 3407  df-un 3409  df-in 3411  df-ss 3418  df-nul 3732  df-if 3882  df-sn 3969  df-pr 3971  df-op 3975  df-br 4403  df-opab 4462  df-xp 4840  df-rel 4841  df-cnv 4842  df-bj-tag 31569  df-bj-1upl 31592
This theorem is referenced by:  bj-2upln0  31617
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