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Metamath Proof Explorer

Theorem bnj1219

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

Ref Expression
Hypotheses bnj1219.1 ⊢ ( 𝜒 ↔ ( 𝜑 ∧ 𝜓 ∧ 𝜁 ) )
bnj1219.2 ⊢ ( 𝜃 ↔ ( 𝜒 ∧ 𝜏 ∧ 𝜂 ) )
Assertion bnj1219 ( 𝜃 → 𝜓 )

Proof

Step Hyp Ref Expression
1 bnj1219.1 ⊢ ( 𝜒 ↔ ( 𝜑 ∧ 𝜓 ∧ 𝜁 ) )
2 bnj1219.2 ⊢ ( 𝜃 ↔ ( 𝜒 ∧ 𝜏 ∧ 𝜂 ) )
3 1 simp2bi ⊢ ( 𝜒 → 𝜓 )
4 2 3 bnj835 ⊢ ( 𝜃 → 𝜓 )