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Theorem reiotacl 4364
 Description: Membership law for descriptions. (Contributed by SF, 21-Aug-2011.)
Assertion
Ref Expression
reiotacl (∃!x A φ → (℩x(x A φ)) A)
Distinct variable group:   x,A
Allowed substitution hint:   φ(x)

Proof of Theorem reiotacl
StepHypRef Expression
1 ssrab2 3351 . . 3 {x A φ} A
21a1i 10 . 2 (∃!x A φ → {x A φ} A)
3 reiotacl2 4363 . 2 (∃!x A φ → (℩x(x A φ)) {x A φ})
42, 3sseldd 3274 1 (∃!x A φ → (℩x(x A φ)) A)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∧ wa 358   ∈ wcel 1710  ∃!wreu 2616  {crab 2618   ⊆ wss 3257  ℩cio 4337 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-eu 2208  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-rex 2620  df-reu 2621  df-rab 2623  df-v 2861  df-sbc 3047  df-nin 3211  df-compl 3212  df-in 3213  df-un 3214  df-ss 3259  df-sn 3741  df-pr 3742  df-uni 3892  df-iota 4339 This theorem is referenced by:  ncfinprop  4474  tfinprop  4489  tccl  6160
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