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Theorem fvprcALT 6899
Description: Alternate proof of fvprc 6898 using ax-pow 5370 instead of ax-pr 5437. (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 1536  wcel 2105  ∃!weu 2565  Vcvv 3477  c0 4338   class class class wbr 5147  cfv 6562
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1791  ax-4 1805  ax-5 1907  ax-6 1964  ax-7 2004  ax-8 2107  ax-9 2115  ax-10 2138  ax-11 2154  ax-12 2174  ax-ext 2705  ax-nul 5311  ax-pow 5370
This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-3an 1088  df-tru 1539  df-fal 1549  df-ex 1776  df-nf 1780  df-sb 2062  df-mo 2537  df-eu 2566  df-clab 2712  df-cleq 2726  df-clel 2813  df-ral 3059  df-rex 3068  df-rab 3433  df-v 3479  df-dif 3965  df-un 3967  df-ss 3979  df-nul 4339  df-if 4531  df-sn 4631  df-pr 4633  df-op 4637  df-uni 4912  df-br 5148  df-iota 6515  df-fv 6570
This theorem is referenced by: (None)
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