Theorem fvprcALT 6913

Description: Alternate proof of fvprc 6912 using ax-pow 5383 instead of ax-pr 5447. (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 6911	. 2 ⊢ (¬ 𝐴 ∈ V → ¬ ∃!𝑥 𝐴𝐹𝑥)
2		tz6.12-2 6908	. 2 ⊢ (¬ ∃!𝑥 𝐴𝐹𝑥 → (𝐹‘𝐴) = ∅)
3	1, 2	syl 17	1 ⊢ (¬ 𝐴 ∈ V → (𝐹‘𝐴) = ∅)

Syntax hints:  ¬ wn 3   → wi 4   = wceq 1537   ∈ wcel 2108  ∃!weu 2571  Vcvv 3488  ∅c0 4352   class class class wbr 5166  ‘cfv 6573

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1793  ax-4 1807  ax-5 1909  ax-6 1967  ax-7 2007  ax-8 2110  ax-9 2118  ax-10 2141  ax-11 2158  ax-12 2178  ax-ext 2711  ax-nul 5324  ax-pow 5383

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 847  df-3an 1089  df-tru 1540  df-fal 1550  df-ex 1778  df-nf 1782  df-sb 2065  df-mo 2543  df-eu 2572  df-clab 2718  df-cleq 2732  df-clel 2819  df-ral 3068  df-rex 3077  df-rab 3444  df-v 3490  df-dif 3979  df-un 3981  df-ss 3993  df-nul 4353  df-if 4549  df-sn 4649  df-pr 4651  df-op 4655  df-uni 4932  df-br 5167  df-iota 6525  df-fv 6581

This theorem is referenced by: (None)