Theorem moeqOLD 3618

Description: Obsolete proof of moeq 3612 as of 24-Sep-2022. (Contributed by NM, 8-Mar-1995.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

Ref	Expression
moeqOLD	⊢ ∃*𝑥 𝑥 = 𝐴

Distinct variable group:   𝑥,𝐴

Proof of Theorem moeqOLD

Step	Hyp	Ref	Expression
1		isset 3427	. . 3 ⊢ (𝐴 ∈ V ↔ ∃𝑥 𝑥 = 𝐴)
2		eueqOLD 3614	. . 3 ⊢ (𝐴 ∈ V ↔ ∃!𝑥 𝑥 = 𝐴)
3	1, 2	sylbb1 229	. 2 ⊢ (∃𝑥 𝑥 = 𝐴 → ∃!𝑥 𝑥 = 𝐴)
4		moeu 2601	. 2 ⊢ (∃*𝑥 𝑥 = 𝐴 ↔ (∃𝑥 𝑥 = 𝐴 → ∃!𝑥 𝑥 = 𝐴))
5	3, 4	mpbir 223	1 ⊢ ∃*𝑥 𝑥 = 𝐴

Syntax hints:   → wi 4   = wceq 1507  ∃wex 1742   ∈ wcel 2050  ∃*wmo 2545  ∃!weu 2582  Vcvv 3415

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1758  ax-4 1772  ax-5 1869  ax-6 1928  ax-7 1965  ax-8 2052  ax-9 2059  ax-10 2079  ax-11 2093  ax-12 2106  ax-ext 2750

This theorem depends on definitions:  df-bi 199  df-an 388  df-or 834  df-tru 1510  df-ex 1743  df-nf 1747  df-sb 2016  df-mo 2547  df-eu 2583  df-clab 2759  df-cleq 2771  df-clel 2846  df-v 3417

This theorem is referenced by: (None)