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Theorem pweq 3725
 Description: Equality theorem for power class. (Contributed by NM, 5-Aug-1993.)
Assertion
Ref Expression
pweq (A = BA = B)

Proof of Theorem pweq
Dummy variable x is distinct from all other variables.
StepHypRef Expression
1 sseq2 3293 . . 3 (A = B → (x Ax B))
21abbidv 2467 . 2 (A = B → {x x A} = {x x B})
3 df-pw 3724 . 2 A = {x x A}
4 df-pw 3724 . 2 B = {x x B}
52, 3, 43eqtr4g 2410 1 (A = BA = B)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   = wceq 1642  {cab 2339   ⊆ wss 3257  ℘cpw 3722 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 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-pw 3724 This theorem is referenced by:  pweqi  3726  pweqd  3727  pw1eq  4143  nnpweq  4523  sfin01  4528  sfindbl  4530  1cvsfin  4542  vfinspsslem1  4550  enpw  6087
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