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Theorem bnj1096 29215
Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Hypotheses
Ref Expression
bnj1096.1  |-  ( ph  ->  A. x ph )
bnj1096.2  |-  ( ps  <->  ( ch  /\  th  /\  ta  /\  ph ) )
Assertion
Ref Expression
bnj1096  |-  ( ps 
->  A. x ps )
Distinct variable groups:    ch, x    ta, x    th, x
Allowed substitution hints:    ph( x)    ps( x)

Proof of Theorem bnj1096
StepHypRef Expression
1 bnj1096.2 . 2  |-  ( ps  <->  ( ch  /\  th  /\  ta  /\  ph ) )
2 ax-17 1627 . . 3  |-  ( ch 
->  A. x ch )
3 ax-17 1627 . . 3  |-  ( th 
->  A. x th )
4 ax-17 1627 . . 3  |-  ( ta 
->  A. x ta )
5 bnj1096.1 . . 3  |-  ( ph  ->  A. x ph )
62, 3, 4, 5bnj982 29211 . 2  |-  ( ( ch  /\  th  /\  ta  /\  ph )  ->  A. x ( ch  /\  th 
/\  ta  /\  ph )
)
71, 6hbxfrbi 1578 1  |-  ( ps 
->  A. x ps )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 178   A.wal 1550    /\ w-bnj17 29112
This theorem is referenced by:  bnj964  29376  bnj981  29383  bnj983  29384  bnj1093  29411  bnj1145  29424
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-11 1762
This theorem depends on definitions:  df-bi 179  df-an 362  df-3an 939  df-ex 1552  df-nf 1555  df-bnj17 29113
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