Theorem bj-issettruALTV

Description: Moved to main as issettru and kept for the comments.

Weak version of isset without ax-ext . (Contributed by BJ, 24-Apr-2024) (Proof modification is discouraged.)

	Ref	Expression
Assertion	bj-issettruALTV	⊢ ( ∃ 𝑥 𝑥 = 𝐴 ↔ 𝐴 ∈ { 𝑦 ∣ ⊤ } )

Proof

Step	Hyp	Ref	Expression
1		iseqsetv-clel	⊢ ( ∃ 𝑥 𝑥 = 𝐴 ↔ ∃ 𝑧 𝑧 = 𝐴 )
2		issettru	⊢ ( ∃ 𝑧 𝑧 = 𝐴 ↔ 𝐴 ∈ { 𝑦 ∣ ⊤ } )
3	1 2	bitri	⊢ ( ∃ 𝑥 𝑥 = 𝐴 ↔ 𝐴 ∈ { 𝑦 ∣ ⊤ } )