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Theorem bnj1352 31708
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-5 1670 . 2  |-  ( ph  ->  A. x ph )
2 bnj1352.1 . 2  |-  ( ps 
->  A. x ps )
31, 2hban 1863 1  |-  ( (
ph  /\  ps )  ->  A. x ( ph  /\ 
ps ) )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    /\ wa 369   A.wal 1367
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1591  ax-4 1602  ax-5 1670  ax-6 1708  ax-7 1728  ax-12 1792
This theorem depends on definitions:  df-bi 185  df-an 371  df-ex 1587  df-nf 1590
This theorem is referenced by:  bnj594  31792  bnj1309  31900
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