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Metamath Proof Explorer

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′ )