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Theorem rp-fakeinunass 36231
 Description: A special case where a mixture of intersection and union appears to conform to a mixed associative law. (Contributed by Richard Penner, 26-Feb-2020.)
Assertion
Ref Expression
rp-fakeinunass

Proof of Theorem rp-fakeinunass
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 rp-fakeanorass 36228 . . 3
21albii 1699 . 2
3 dfss2 3407 . 2
4 dfcleq 2465 . . 3
5 elun 3565 . . . . . 6
6 elin 3608 . . . . . . 7
76orbi1i 529 . . . . . 6
85, 7bitri 257 . . . . 5
9 elin 3608 . . . . . 6
10 elun 3565 . . . . . . 7
1110anbi2i 708 . . . . . 6
129, 11bitri 257 . . . . 5
138, 12bibi12i 322 . . . 4
1413albii 1699 . . 3
154, 14bitri 257 . 2
162, 3, 153bitr4i 285 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 189   wo 375   wa 376  wal 1450   wceq 1452   wcel 1904   cun 3388   cin 3389   wss 3390 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 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-clab 2458  df-cleq 2464  df-clel 2467  df-nfc 2601  df-v 3033  df-un 3395  df-in 3397  df-ss 3404 This theorem is referenced by:  rp-fakeuninass  36232
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