Theorem bnj1224 30872

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

Hypothesis

Ref	Expression
bnj1224.1	|- -. ( th /\ ta /\ et )

Assertion

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

Proof of Theorem bnj1224

Step	Hyp	Ref	Expression
1		bnj1224.1	. . 3 |- -. ( th /\ ta /\ et )
2		df-3an 1039	. . 3 |- ( ( th /\ ta /\ et ) <-> ( ( th /\ ta ) /\ et ) )
3	1, 2	mtbi 312	. 2 |- -. ( ( th /\ ta ) /\ et )
4	3	imnani 439	1 |- ( ( th /\ ta ) -> -. et )

Syntax hints:   -. wn 3   -> wi 4   /\ wa 384   /\ w3a 1037

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 197  df-an 386  df-3an 1039

This theorem is referenced by:  bnj1204  31080  bnj1279  31086