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Metamath Proof Explorer

Theorem bnj31

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

Ref Expression
Hypotheses bnj31.1 ⊢ ( 𝜑 → ∃ 𝑥 ∈ 𝐴 𝜓 )
bnj31.2 ⊢ ( 𝜓 → 𝜒 )
Assertion bnj31 ( 𝜑 → ∃ 𝑥 ∈ 𝐴 𝜒 )

Proof

Step Hyp Ref Expression
1 bnj31.1 ⊢ ( 𝜑 → ∃ 𝑥 ∈ 𝐴 𝜓 )
2 bnj31.2 ⊢ ( 𝜓 → 𝜒 )
3 2 reximi ⊢ ( ∃ 𝑥 ∈ 𝐴 𝜓 → ∃ 𝑥 ∈ 𝐴 𝜒 )
4 1 3 syl ⊢ ( 𝜑 → ∃ 𝑥 ∈ 𝐴 𝜒 )