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Theorem p6eq 4238
 Description: Equality theorem for P6 operation. (Contributed by SF, 12-Jan-2015.)
Assertion
Ref Expression
p6eq P6 P6

Proof of Theorem p6eq
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 sseq2 3293 . . 3 k k
21abbidv 2467 . 2 k k
3 df-p6 4191 . 2 P6 k
4 df-p6 4191 . 2 P6 k
52, 3, 43eqtr4g 2410 1 P6 P6
 Colors of variables: wff setvar class Syntax hints:   wi 4   wceq 1642  cab 2339  cvv 2859   wss 3257  csn 3737   k cxpk 4174   P6 cp6 4178 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 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 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  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-v 2861  df-nin 3211  df-compl 3212  df-in 3213  df-ss 3259  df-p6 4191 This theorem is referenced by:  p6eqi  4239  p6eqd  4240  p6exg  4290
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