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Theorem bnj1276 29163
Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Hypotheses
Ref Expression
bnj1276.1  |-  ( ph  ->  A. x ph )
bnj1276.2  |-  ( ps 
->  A. x ps )
bnj1276.3  |-  ( ch 
->  A. x ch )
bnj1276.4  |-  ( th  <->  (
ph  /\  ps  /\  ch ) )
Assertion
Ref Expression
bnj1276  |-  ( th 
->  A. x th )

Proof of Theorem bnj1276
StepHypRef Expression
1 bnj1276.4 . 2  |-  ( th  <->  (
ph  /\  ps  /\  ch ) )
2 bnj1276.1 . . 3  |-  ( ph  ->  A. x ph )
3 bnj1276.2 . . 3  |-  ( ps 
->  A. x ps )
4 bnj1276.3 . . 3  |-  ( ch 
->  A. x ch )
52, 3, 4hb3an 1771 . 2  |-  ( (
ph  /\  ps  /\  ch )  ->  A. x ( ph  /\ 
ps  /\  ch )
)
61, 5hbxfrbi 1558 1  |-  ( th 
->  A. x th )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 176    /\ w3a 934   A.wal 1530
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-11 1727
This theorem depends on definitions:  df-bi 177  df-an 360  df-3an 936
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