Mathbox for BJ < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  bj-nuliotaALT Structured version   Visualization version   Unicode version

Theorem bj-nuliotaALT 31694
 Description: Alternate proof of bj-nuliota 31693. Note that this alternate proof uses the fact that evaluates to when there is no satisfying (iotanul 5568). This is an implementation detail of the encoding currently used in set.mm and should be avoided. (Contributed by BJ, 30-Nov-2019.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
bj-nuliotaALT
Distinct variable group:   ,

Proof of Theorem bj-nuliotaALT
StepHypRef Expression
1 0ss 3766 . 2
2 iotassuni 5569 . . 3
3 eq0 3738 . . . . . . 7
43bicomi 207 . . . . . 6
54abbii 2587 . . . . 5
65unieqi 4199 . . . 4
7 df-sn 3960 . . . . . 6
87eqcomi 2480 . . . . 5
98unieqi 4199 . . . 4
10 0ex 4528 . . . . 5
1110unisn 4205 . . . 4
126, 9, 113eqtri 2497 . . 3
132, 12sseqtri 3450 . 2
141, 13eqssi 3434 1
 Colors of variables: wff setvar class Syntax hints:   wn 3  wal 1450   wceq 1452  cab 2457  c0 3722  csn 3959  cuni 4190  cio 5551 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-10 1932  ax-11 1937  ax-12 1950  ax-13 2104  ax-ext 2451  ax-nul 4527 This theorem depends on definitions:  df-bi 190  df-or 377  df-an 378  df-tru 1455  df-ex 1672  df-nf 1676  df-sb 1806  df-eu 2323  df-clab 2458  df-cleq 2464  df-clel 2467  df-nfc 2601  df-ne 2643  df-ral 2761  df-rex 2762  df-v 3033  df-sbc 3256  df-dif 3393  df-un 3395  df-in 3397  df-ss 3404  df-nul 3723  df-sn 3960  df-pr 3962  df-uni 4191  df-iota 5553 This theorem is referenced by: (None)
 Copyright terms: Public domain W3C validator