Theorem wl-motae

Description: Change bound variable. Uses only Tarski's FOL axiom schemes. Part of Lemma 7 of KalishMontague p. 86. (Contributed by Wolf Lammen, 5-Mar-2023)

	Ref	Expression
Assertion	wl-motae	⊢ ( ∃* 𝑢 ⊤ → ∀ 𝑥 𝑦 = 𝑧 )

Proof

Step	Hyp	Ref	Expression
1		wl-cbvmotv	⊢ ( ∃* 𝑢 ⊤ → ∃* 𝑣 ⊤ )
2		wl-moteq	⊢ ( ∃* 𝑣 ⊤ → 𝑦 = 𝑧 )
3	2	alrimiv	⊢ ( ∃* 𝑣 ⊤ → ∀ 𝑥 𝑦 = 𝑧 )
4	1 3	syl	⊢ ( ∃* 𝑢 ⊤ → ∀ 𝑥 𝑦 = 𝑧 )