Theorem fvprcALT 6868

Description: Alternate proof of fvprc 6867 using ax-pow 5335 instead of ax-pr 5402. (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 6866	. 2 ⊢ (¬ 𝐴 ∈ V → ¬ ∃!𝑥 𝐴𝐹𝑥)
2		tz6.12-2 6863	. 2 ⊢ (¬ ∃!𝑥 𝐴𝐹𝑥 → (𝐹‘𝐴) = ∅)
3	1, 2	syl 17	1 ⊢ (¬ 𝐴 ∈ V → (𝐹‘𝐴) = ∅)

Syntax hints:  ¬ wn 3   → wi 4   = wceq 1540   ∈ wcel 2108  ∃!weu 2567  Vcvv 3459  ∅c0 4308   class class class wbr 5119  ‘cfv 6530

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 2707  ax-nul 5276  ax-pow 5335

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-3an 1088  df-tru 1543  df-fal 1553  df-ex 1780  df-nf 1784  df-sb 2065  df-mo 2539  df-eu 2568  df-clab 2714  df-cleq 2727  df-clel 2809  df-ral 3052  df-rex 3061  df-rab 3416  df-v 3461  df-dif 3929  df-un 3931  df-ss 3943  df-nul 4309  df-if 4501  df-sn 4602  df-pr 4604  df-op 4608  df-uni 4884  df-br 5120  df-iota 6483  df-fv 6538

This theorem is referenced by: (None)