Theorem alequexv

Description: Version of equs4v with its consequence simplified by exsimpr . (Contributed by BJ, 9-Nov-2021)

	Ref	Expression
Assertion	alequexv	⊢ ( ∀ 𝑥 ( 𝑥 = 𝑦 → 𝜑 ) → ∃ 𝑥 𝜑 )

Proof

Step	Hyp	Ref	Expression
1		ax6ev	⊢ ∃ 𝑥 𝑥 = 𝑦
2		exim	⊢ ( ∀ 𝑥 ( 𝑥 = 𝑦 → 𝜑 ) → ( ∃ 𝑥 𝑥 = 𝑦 → ∃ 𝑥 𝜑 ) )
3	1 2	mpi	⊢ ( ∀ 𝑥 ( 𝑥 = 𝑦 → 𝜑 ) → ∃ 𝑥 𝜑 )