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Theorem p6exg 4290
 Description: The P6 operator applied to a set yields a set. (Contributed by SF, 13-Jan-2015.)
Assertion
Ref Expression
p6exg P6

Proof of Theorem p6exg
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 p6eq 4238 . . 3 P6 P6
21eleq1d 2419 . 2 P6 P6
3 ax-typlower 4086 . . 3
4 dfcleq 2347 . . . . . . 7 P6 P6
5 vex 2862 . . . . . . . . . 10
6 elp6 4263 . . . . . . . . . 10 P6
75, 6ax-mp 8 . . . . . . . . 9 P6
87bibi2i 304 . . . . . . . 8 P6
98albii 1566 . . . . . . 7 P6
104, 9bitri 240 . . . . . 6 P6
1110biimpri 197 . . . . 5 P6
12 vex 2862 . . . . 5
1311, 12syl6eqelr 2442 . . . 4 P6
1413exlimiv 1634 . . 3 P6
153, 14ax-mp 8 . 2 P6
162, 15vtoclg 2914 1 P6
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 176  wal 1540  wex 1541   wceq 1642   wcel 1710  cvv 2859  csn 3737  copk 4057   P6 cp6 4178 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334  ax-nin 4078  ax-typlower 4086  ax-sn 4087 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-nan 1288  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-ne 2518  df-ral 2619  df-rex 2620  df-v 2861  df-nin 3211  df-compl 3212  df-in 3213  df-un 3214  df-dif 3215  df-ss 3259  df-nul 3551  df-sn 3741  df-pr 3742  df-opk 4058  df-xpk 4185  df-p6 4191 This theorem is referenced by:  uni1exg  4292  imakexg  4299
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