Theorem bnj1198

Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011) (New usage is discouraged.)

	Ref	Expression
Hypotheses	bnj1198.1	⊢ ( 𝜑 → ∃ 𝑥 𝜓 )
	bnj1198.2	⊢ ( 𝜓′ ↔ 𝜓 )
Assertion	bnj1198	⊢ ( 𝜑 → ∃ 𝑥 𝜓′ )

Proof

Step	Hyp	Ref	Expression
1		bnj1198.1	⊢ ( 𝜑 → ∃ 𝑥 𝜓 )
2		bnj1198.2	⊢ ( 𝜓′ ↔ 𝜓 )
3	2	exbii	⊢ ( ∃ 𝑥 𝜓′ ↔ ∃ 𝑥 𝜓 )
4	1 3	sylibr	⊢ ( 𝜑 → ∃ 𝑥 𝜓′ )