Theorem iseqsetvlem 2804

Description: Lemma for iseqsetv-cleq 2805. (Contributed by Wolf Lammen, 17-Aug-2025.) (Proof modification is discouraged.)

Assertion

Ref	Expression
iseqsetvlem	⊢ (∃𝑥 𝑥 = 𝐴 ↔ ∃𝑧 𝑧 = 𝐴)

Distinct variable group:   𝑥,𝑧,𝐴

Proof of Theorem iseqsetvlem

Step	Hyp	Ref	Expression
1		eqeq1 2740	. 2 ⊢ (𝑥 = 𝑧 → (𝑥 = 𝐴 ↔ 𝑧 = 𝐴))
2	1	cbvexvw 2036	1 ⊢ (∃𝑥 𝑥 = 𝐴 ↔ ∃𝑧 𝑧 = 𝐴)

Syntax hints:   ↔ wb 206   = wceq 1540  ∃wex 1779

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-9 2118  ax-ext 2707

This theorem depends on definitions:  df-bi 207  df-an 396  df-ex 1780  df-cleq 2728

This theorem is referenced by:  iseqsetv-cleq  2805