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Theorem pm14.18 44383
Description: Theorem *14.18 in [WhiteheadRussell] p. 189. (Contributed by Andrew Salmon, 11-Jul-2011.)
Assertion
Ref Expression
pm14.18 (∃!𝑥𝜑 → (∀𝑥𝜓[(℩𝑥𝜑) / 𝑥]𝜓))

Proof of Theorem pm14.18
StepHypRef Expression
1 iotaexeu 44373 . 2 (∃!𝑥𝜑 → (℩𝑥𝜑) ∈ V)
2 spsbc 3804 . 2 ((℩𝑥𝜑) ∈ V → (∀𝑥𝜓[(℩𝑥𝜑) / 𝑥]𝜓))
31, 2syl 17 1 (∃!𝑥𝜑 → (∀𝑥𝜓[(℩𝑥𝜑) / 𝑥]𝜓))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1533  wcel 2104  ∃!weu 2564  Vcvv 3477  [wsbc 3791  cio 6508
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1790  ax-4 1804  ax-5 1906  ax-6 1963  ax-7 2003  ax-8 2106  ax-9 2114  ax-10 2137  ax-12 2173  ax-ext 2704
This theorem depends on definitions:  df-bi 207  df-an 396  df-or 847  df-tru 1538  df-ex 1775  df-nf 1779  df-sb 2061  df-mo 2536  df-eu 2565  df-clab 2711  df-cleq 2725  df-clel 2812  df-v 3479  df-sbc 3792  df-un 3968  df-ss 3980  df-sn 4631  df-pr 4633  df-uni 4915  df-iota 6510
This theorem is referenced by: (None)
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