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Theorem bnj1352 29176
Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Hypothesis
Ref Expression
bnj1352.1  |-  ( ps 
->  A. x ps )
Assertion
Ref Expression
bnj1352  |-  ( (
ph  /\  ps )  ->  A. x ( ph  /\ 
ps ) )
Distinct variable group:    ph, x
Allowed substitution hint:    ps( x)

Proof of Theorem bnj1352
StepHypRef Expression
1 ax-17 1606 . 2  |-  ( ph  ->  A. x ph )
2 bnj1352.1 . 2  |-  ( ps 
->  A. x ps )
31, 2hban 1748 1  |-  ( (
ph  /\  ps )  ->  A. x ( ph  /\ 
ps ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 358   A.wal 1530
This theorem is referenced by:  bnj594  29260  bnj1309  29368
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
  Copyright terms: Public domain W3C validator