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Theorem rmobidv 2742
Description: Formula-building rule for restricted existential quantifier (deduction rule). (Contributed by NM, 16-Jun-2017.)
Hypothesis
Ref Expression
rmobidv.1  |-  ( ph  ->  ( ps  <->  ch )
)
Assertion
Ref Expression
rmobidv  |-  ( ph  ->  ( E* x  e.  A ps  <->  E* x  e.  A ch ) )
Distinct variable group:    ph, x
Allowed substitution hints:    ps( x)    ch( x)    A( x)

Proof of Theorem rmobidv
StepHypRef Expression
1 rmobidv.1 . . 3  |-  ( ph  ->  ( ps  <->  ch )
)
21adantr 451 . 2  |-  ( (
ph  /\  x  e.  A )  ->  ( ps 
<->  ch ) )
32rmobidva 2741 1  |-  ( ph  ->  ( E* x  e.  A ps  <->  E* x  e.  A ch ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 176    e. wcel 1696   E*wrmo 2559
This theorem is referenced by:  rmoeqd  2760  brdom7disj  8172
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-11 1727
This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1532  df-nf 1535  df-eu 2160  df-mo 2161  df-rmo 2564
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