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Metamath Proof Explorer

Theorem bnj1224

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

Ref Expression
Hypothesis bnj1224.1 ⊢ ¬ ( 𝜃 ∧ 𝜏 ∧ 𝜂 )
Assertion bnj1224 ( ( 𝜃 ∧ 𝜏 ) → ¬ 𝜂 )

Proof

Step Hyp Ref Expression
1 bnj1224.1 ⊢ ¬ ( 𝜃 ∧ 𝜏 ∧ 𝜂 )
2 df-3an ⊢ ( ( 𝜃 ∧ 𝜏 ∧ 𝜂 ) ↔ ( ( 𝜃 ∧ 𝜏 ) ∧ 𝜂 ) )
3 1 2 mtbi ⊢ ¬ ( ( 𝜃 ∧ 𝜏 ) ∧ 𝜂 )
4 3 imnani ⊢ ( ( 𝜃 ∧ 𝜏 ) → ¬ 𝜂 )