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 
|- -. ( th /\ ta /\ et )
Assertion bnj1224 
|- ( ( th /\ ta ) -> -. et )

Proof

Step Hyp Ref Expression
1 bnj1224.1 
 |-  -. ( th /\ ta /\ et )
2 df-3an 
 |-  ( ( th /\ ta /\ et ) <-> ( ( th /\ ta ) /\ et ) )
3 1 2 mtbi 
 |-  -. ( ( th /\ ta ) /\ et )
4 3 imnani 
 |-  ( ( th /\ ta ) -> -. et )