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Metamath Proof Explorer

Theorem bnj132

Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011) (Proof shortened by Andrew Salmon, 26-Jun-2011) (New usage is discouraged.)

Ref Expression
Hypothesis bnj132.1 ⊢ φ ↔ ∃ x ψ → χ
Assertion bnj132 ⊢ φ ↔ ψ → ∃ x χ

Proof

Step Hyp Ref Expression
1 bnj132.1 ⊢ φ ↔ ∃ x ψ → χ
2 19.37v ⊢ ∃ x ψ → χ ↔ ψ → ∃ x χ
3 1 2 bitri ⊢ φ ↔ ψ → ∃ x χ