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Theorem bj-1upln0 31673
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 31662 . 2  |- (| A|)  =  ( { (/) }  X. tag  A
)
2 0nep0 4572 . . . 4  |-  (/)  =/=  { (/)
}
32necomi 2697 . . 3  |-  { (/) }  =/=  (/)
4 bj-tagn0 31643 . . 3  |- tag  A  =/=  (/)
5 xpnz 5262 . . . 4  |-  ( ( { (/) }  =/=  (/)  /\ tag  A  =/=  (/) )  <->  ( { (/)
}  X. tag  A )  =/=  (/) )
65biimpi 199 . . 3  |-  ( ( { (/) }  =/=  (/)  /\ tag  A  =/=  (/) )  ->  ( { (/) }  X. tag  A
)  =/=  (/) )
73, 4, 6mp2an 686 . 2  |-  ( {
(/) }  X. tag  A )  =/=  (/)
81, 7eqnetri 2713 1  |- (| A|)  =/=  (/)
Colors of variables: wff setvar class
Syntax hints:    /\ wa 376    =/= wne 2641   (/)c0 3722   {csn 3959    X. cxp 4837  tag bj-ctag 31638  (|bj-c1upl 31661
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1677  ax-4 1690  ax-5 1766  ax-6 1813  ax-7 1859  ax-9 1913  ax-10 1932  ax-11 1937  ax-12 1950  ax-13 2104  ax-ext 2451  ax-sep 4518  ax-nul 4527  ax-pr 4639
This theorem depends on definitions:  df-bi 190  df-or 377  df-an 378  df-3an 1009  df-tru 1455  df-ex 1672  df-nf 1676  df-sb 1806  df-eu 2323  df-mo 2324  df-clab 2458  df-cleq 2464  df-clel 2467  df-nfc 2601  df-ne 2643  df-ral 2761  df-rex 2762  df-rab 2765  df-v 3033  df-dif 3393  df-un 3395  df-in 3397  df-ss 3404  df-nul 3723  df-if 3873  df-sn 3960  df-pr 3962  df-op 3966  df-br 4396  df-opab 4455  df-xp 4845  df-rel 4846  df-cnv 4847  df-bj-tag 31639  df-bj-1upl 31662
This theorem is referenced by:  bj-2upln0  31687
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