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Theorem f1opw 6301
 Description: A one-to-one mapping induces a one-to-one mapping on power sets. (Contributed by Stefan O'Rear, 18-Nov-2014.) (Revised by Mario Carneiro, 26-Jun-2015.)
Assertion
Ref Expression
f1opw
Distinct variable groups:   ,   ,   ,

Proof of Theorem f1opw
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 id 21 . 2
2 dff1o3 5682 . . . 4
32simprbi 452 . . 3
4 vex 2961 . . . 4
54funimaex 5533 . . 3
63, 5syl 16 . 2
7 f1ofun 5678 . . 3
8 vex 2961 . . . 4
98funimaex 5533 . . 3
107, 9syl 16 . 2
111, 6, 10f1opw2 6300 1
 Colors of variables: wff set class Syntax hints:   wi 4   wcel 1726  cvv 2958  cpw 3801   cmpt 4268  ccnv 4879  cima 4883   wfun 5450  wfo 5454  wf1o 5455 This theorem is referenced by:  ackbij2lem2  8122 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-14 1730  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419  ax-rep 4322  ax-sep 4332  ax-nul 4340  ax-pr 4405 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-eu 2287  df-mo 2288  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ne 2603  df-ral 2712  df-rex 2713  df-rab 2716  df-v 2960  df-dif 3325  df-un 3327  df-in 3329  df-ss 3336  df-nul 3631  df-if 3742  df-pw 3803  df-sn 3822  df-pr 3823  df-op 3825  df-br 4215  df-opab 4269  df-mpt 4270  df-id 4500  df-xp 4886  df-rel 4887  df-cnv 4888  df-co 4889  df-dm 4890  df-rn 4891  df-res 4892  df-ima 4893  df-fun 5458  df-fn 5459  df-f 5460  df-f1 5461  df-fo 5462  df-f1o 5463
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