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Theorem fvprcALT 6899
Description: Alternate proof of fvprc 6898 using ax-pow 5365 instead of ax-pr 5432. (Contributed by NM, 20-May-1998.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
fvprcALT 𝐴 ∈ V → (𝐹𝐴) = ∅)

Proof of Theorem fvprcALT
Dummy variable 𝑥 is distinct from all other variables.
StepHypRef Expression
1 brprcneuALT 6897 . 2 𝐴 ∈ V → ¬ ∃!𝑥 𝐴𝐹𝑥)
2 tz6.12-2 6894 . 2 (¬ ∃!𝑥 𝐴𝐹𝑥 → (𝐹𝐴) = ∅)
31, 2syl 17 1 𝐴 ∈ V → (𝐹𝐴) = ∅)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4   = wceq 1540  wcel 2108  ∃!weu 2568  Vcvv 3480  c0 4333   class class class wbr 5143  cfv 6561
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2007  ax-8 2110  ax-9 2118  ax-10 2141  ax-11 2157  ax-12 2177  ax-ext 2708  ax-nul 5306  ax-pow 5365
This theorem depends on definitions:  df-bi 207  df-an 396  df-or 849  df-3an 1089  df-tru 1543  df-fal 1553  df-ex 1780  df-nf 1784  df-sb 2065  df-mo 2540  df-eu 2569  df-clab 2715  df-cleq 2729  df-clel 2816  df-ral 3062  df-rex 3071  df-rab 3437  df-v 3482  df-dif 3954  df-un 3956  df-ss 3968  df-nul 4334  df-if 4526  df-sn 4627  df-pr 4629  df-op 4633  df-uni 4908  df-br 5144  df-iota 6514  df-fv 6569
This theorem is referenced by: (None)
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