Theorem tz6.12-2OLD 6884

Description: Obsolete version of tz6.12-2 6883 as of 25-Jan-2026. (Contributed by NM, 30-Apr-2004.) (Proof shortened by Mario Carneiro, 31-Aug-2015.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

Ref	Expression
tz6.12-2OLD	⊢ (¬ ∃!𝑥 𝐴𝐹𝑥 → (𝐹‘𝐴) = ∅)

Distinct variable groups:   𝑥,𝐹   𝑥,𝐴

Proof of Theorem tz6.12-2OLD

Step	Hyp	Ref	Expression
1		df-fv 6555	. 2 ⊢ (𝐹‘𝐴) = (℩𝑥𝐴𝐹𝑥)
2		iotanul 6526	. 2 ⊢ (¬ ∃!𝑥 𝐴𝐹𝑥 → (℩𝑥𝐴𝐹𝑥) = ∅)
3	1, 2	eqtrid 2810	1 ⊢ (¬ ∃!𝑥 𝐴𝐹𝑥 → (𝐹‘𝐴) = ∅)

This proof depends on syntax axioms:  ¬ wn 3   → wi 4   = wceq 1569  ∃!weu 2596  ∅c0 4281   class class class wbr 5106  ℩cio 6499  ‘cfv 6547

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1827  ax-4 1841  ax-5 1944  ax-6 2001  ax-7 2042  ax-8 2148  ax-9 2156  ax-10 2179  ax-11 2196  ax-12 2215  ax-ext 2735

This proof depends on definitions:  df-bi 210  df-an 402  df-or 862  df-tru 1572  df-fal 1582  df-ex 1812  df-nf 1816  df-sb 2101  df-mo 2567  df-eu 2597  df-clab 2742  df-cleq 2755  df-clel 2839  df-v 3456  df-ss 3901  df-dif 4050  df-nul 4282  df-sn 4589  df-uni 4871  df-iota 6501  df-fv 6555

This theorem is used by: (None)