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Theorem bnj1224 29247
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
StepHypRef Expression
1 bnj1224.1 . . 3  |-  -.  ( th  /\  ta  /\  et )
2 df-3an 939 . . 3  |-  ( ( th  /\  ta  /\  et )  <->  ( ( th 
/\  ta )  /\  et ) )
31, 2mtbi 291 . 2  |-  -.  (
( th  /\  ta )  /\  et )
43imnani 414 1  |-  ( ( th  /\  ta )  ->  -.  et )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    /\ wa 360    /\ w3a 937
This theorem is referenced by:  bnj1204  29455  bnj1279  29461
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 179  df-an 362  df-3an 939
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