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Theorem tz6.12-1 6870
Description: Function value. Theorem 6.12(1) of [TakeutiZaring] p. 27. (Contributed by NM, 30-Apr-2004.) (Proof shortened by SN, 23-Dec-2024.)
Assertion
Ref Expression
tz6.12-1 ((𝐴𝐹𝑦 ∧ ∃!𝑦 𝐴𝐹𝑦) → (𝐹𝐴) = 𝑦)
Distinct variable groups:   𝑦,𝐹   𝑦,𝐴

Proof of Theorem tz6.12-1
StepHypRef Expression
1 tz6.12c 6869 . 2 (∃!𝑦 𝐴𝐹𝑦 → ((𝐹𝐴) = 𝑦𝐴𝐹𝑦))
21biimparc 481 1 ((𝐴𝐹𝑦 ∧ ∃!𝑦 𝐴𝐹𝑦) → (𝐹𝐴) = 𝑦)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 397   = wceq 1542  ∃!weu 2567   class class class wbr 5110  cfv 6501
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2109  ax-9 2117  ax-10 2138  ax-12 2172  ax-ext 2708
This theorem depends on definitions:  df-bi 206  df-an 398  df-or 847  df-tru 1545  df-ex 1783  df-nf 1787  df-sb 2069  df-mo 2539  df-eu 2568  df-clab 2715  df-cleq 2729  df-clel 2815  df-v 3450  df-un 3920  df-in 3922  df-ss 3932  df-sn 4592  df-pr 4594  df-uni 4871  df-iota 6453  df-fv 6509
This theorem is referenced by:  tz6.12  6872  tz6.12cOLD  6874  funbrfv  6898  setrec2lem2  47213
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