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Theorem eubi 27636
Description: Theorem *14.271 in [WhiteheadRussell] p. 192. (Contributed by Andrew Salmon, 11-Jul-2011.)
Assertion
Ref Expression
eubi  |-  ( A. x ( ph  <->  ps )  ->  ( E! x ph  <->  E! x ps ) )

Proof of Theorem eubi
StepHypRef Expression
1 nfa1 1756 . 2  |-  F/ x A. x ( ph  <->  ps )
2 sp 1716 . 2  |-  ( A. x ( ph  <->  ps )  ->  ( ph  <->  ps )
)
31, 2eubid 2150 1  |-  ( A. x ( ph  <->  ps )  ->  ( E! x ph  <->  E! x ps ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 176   A.wal 1527   E!weu 2143
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-11 1715
This theorem depends on definitions:  df-bi 177  df-ex 1529  df-nf 1532  df-eu 2147
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