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Theorem reiotacl2 4363
 Description: Membership law for descriptions. (Contributed by SF, 21-Aug-2011.)
Assertion
Ref Expression
reiotacl2 (∃!x A φ → (℩x(x A φ)) {x A φ})

Proof of Theorem reiotacl2
StepHypRef Expression
1 df-reu 2621 . . 3 (∃!x A φ∃!x(x A φ))
2 iotacl 4362 . . 3 (∃!x(x A φ) → (℩x(x A φ)) {x (x A φ)})
31, 2sylbi 187 . 2 (∃!x A φ → (℩x(x A φ)) {x (x A φ)})
4 df-rab 2623 . 2 {x A φ} = {x (x A φ)}
53, 4syl6eleqr 2444 1 (∃!x A φ → (℩x(x A φ)) {x A φ})
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∧ wa 358   ∈ wcel 1710  ∃!weu 2204  {cab 2339  ∃!wreu 2616  {crab 2618  ℩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-un 3214  df-sn 3741  df-pr 3742  df-uni 3892  df-iota 4339 This theorem is referenced by:  reiotacl  4364
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