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Theorem bnj1350 28903
Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Hypothesis
Ref Expression
bnj1350.1  |-  ( ch 
->  A. x ch )
Assertion
Ref Expression
bnj1350  |-  ( (
ph  /\  ps  /\  ch )  ->  A. x ( ph  /\ 
ps  /\  ch )
)
Distinct variable groups:    ph, x    ps, x
Allowed substitution hint:    ch( x)

Proof of Theorem bnj1350
StepHypRef Expression
1 ax-17 1623 . 2  |-  ( ph  ->  A. x ph )
2 ax-17 1623 . 2  |-  ( ps 
->  A. x ps )
3 bnj1350.1 . 2  |-  ( ch 
->  A. x ch )
41, 2, 3hb3an 1848 1  |-  ( (
ph  /\  ps  /\  ch )  ->  A. x ( ph  /\ 
ps  /\  ch )
)
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ w3a 936   A.wal 1546
This theorem is referenced by:  bnj911  29009  bnj1093  29055
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1662  ax-8 1683  ax-11 1757
This theorem depends on definitions:  df-bi 178  df-an 361  df-3an 938  df-ex 1548  df-nf 1551
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