Theorem bj-cbvexivw

Description: Change bound variable. This is to cbvexvw what cbvalivw is to cbvalvw . TODO: move after cbvalivw . (Contributed by BJ, 17-Mar-2020)

	Ref	Expression
Hypothesis	bj-cbvexivw.1	⊢ ( 𝑦 = 𝑥 → ( 𝜑 → 𝜓 ) )
Assertion	bj-cbvexivw	⊢ ( ∃ 𝑥 𝜑 → ∃ 𝑦 𝜓 )

Proof

Step	Hyp	Ref	Expression
1		bj-cbvexivw.1	⊢ ( 𝑦 = 𝑥 → ( 𝜑 → 𝜓 ) )
2		ax5e	⊢ ( ∃ 𝑥 ∃ 𝑦 𝜓 → ∃ 𝑦 𝜓 )
3		ax-5	⊢ ( 𝜑 → ∀ 𝑦 𝜑 )
4	2 3 1	bj-cbvexiw	⊢ ( ∃ 𝑥 𝜑 → ∃ 𝑦 𝜓 )