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Theorem eubi 26803
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 1719 . 2  |-  F/ x A. x ( ph  <->  ps )
2 ax-4 1692 . 2  |-  ( A. x ( ph  <->  ps )  ->  ( ph  <->  ps )
)
31, 2eubid 2121 1  |-  ( A. x ( ph  <->  ps )  ->  ( E! x ph  <->  E! x ps ) )
Colors of variables: wff set class
Syntax hints:    -> wi 6    <-> wb 178   A.wal 1532   E!weu 2114
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-6 1534  ax-gen 1536  ax-17 1628  ax-4 1692
This theorem depends on definitions:  df-bi 179  df-ex 1538  df-nf 1540  df-eu 2118
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