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Metamath Proof Explorer

Theorem bnj593

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

Ref Expression
Hypotheses bnj593.1 ⊢ φ → ∃ x ψ
bnj593.2 ⊢ ψ → χ
Assertion bnj593 ⊢ φ → ∃ x χ

Proof

Step Hyp Ref Expression
1 bnj593.1 ⊢ φ → ∃ x ψ
2 bnj593.2 ⊢ ψ → χ
3 2 eximi ⊢ ∃ x ψ → ∃ x χ
4 1 3 syl ⊢ φ → ∃ x χ