Theorem fvprcALT 6820

Description: Alternate proof of fvprc 6819 using ax-pow 5294 instead of ax-pr 5362. (Contributed by NM, 20-May-1998.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

Ref	Expression
fvprcALT	⊢ (¬ 𝐴 ∈ V → (𝐹‘𝐴) = ∅)

Proof of Theorem fvprcALT

Dummy variable 𝑥 is distinct from all other variables.

Step	Hyp	Ref	Expression
1		brprcneuALT 6818	. 2 ⊢ (¬ 𝐴 ∈ V → ¬ ∃!𝑥 𝐴𝐹𝑥)
2		tz6.12-2 6814	. 2 ⊢ (¬ ∃!𝑥 𝐴𝐹𝑥 → (𝐹‘𝐴) = ∅)
3	1, 2	syl 17	1 ⊢ (¬ 𝐴 ∈ V → (𝐹‘𝐴) = ∅)

Syntax hints:  ¬ wn 3   → wi 4   = wceq 1547   ∈ wcel 2119  ∃!weu 2572  Vcvv 3431  ∅c0 4261   class class class wbr 5072  ‘cfv 6485

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1802  ax-4 1816  ax-5 1917  ax-6 1974  ax-7 2015  ax-8 2121  ax-9 2129  ax-ext 2711  ax-nul 5228  ax-pow 5294

This theorem depends on definitions:  df-bi 208  df-an 397  df-or 854  df-3an 1094  df-tru 1550  df-fal 1560  df-ex 1787  df-sb 2074  df-mo 2543  df-eu 2573  df-clab 2718  df-cleq 2731  df-clel 2814  df-ne 2935  df-rab 3392  df-v 3433  df-dif 3886  df-un 3888  df-ss 3900  df-nul 4262  df-if 4455  df-sn 4556  df-pr 4558  df-op 4562  df-uni 4839  df-br 5073  df-iota 6441  df-fv 6493

This theorem is referenced by: (None)