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Theorem bnj1351 29125
Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Hypothesis
Ref Expression
bnj1351.1  |-  ( ph  ->  A. x ph )
Assertion
Ref Expression
bnj1351  |-  ( (
ph  /\  ps )  ->  A. x ( ph  /\ 
ps ) )
Distinct variable group:    ps, x
Allowed substitution hint:    ph( x)

Proof of Theorem bnj1351
StepHypRef Expression
1 bnj1351.1 . 2  |-  ( ph  ->  A. x ph )
2 ax-17 1626 . 2  |-  ( ps 
->  A. x ps )
31, 2hban 1850 1  |-  ( (
ph  /\  ps )  ->  A. x ( ph  /\ 
ps ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 359   A.wal 1549
This theorem is referenced by:  bnj1373  29326  bnj1445  29340
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-11 1761
This theorem depends on definitions:  df-bi 178  df-an 361  df-ex 1551  df-nf 1554
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