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 ¬ ( 𝜃𝜏𝜂 )
Assertion bnj1224 ( ( 𝜃𝜏 ) → ¬ 𝜂 )

Proof

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