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Theorem rmobidv 2645
Description: Formula-building rule for restricted existential quantifier (deduction form). (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 274 . 2  |-  ( (
ph  /\  x  e.  A )  ->  ( ps 
<->  ch ) )
32rmobidva 2644 1  |-  ( ph  ->  ( E* x  e.  A  ps  <->  E* x  e.  A  ch )
)
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 104    e. wcel 2128   E*wrmo 2438
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1427  ax-gen 1429  ax-ie1 1473  ax-ie2 1474  ax-4 1490  ax-17 1506  ax-ial 1514
This theorem depends on definitions:  df-bi 116  df-nf 1441  df-eu 2009  df-mo 2010  df-rmo 2443
This theorem is referenced by:  rmoeqd  2663  disjxp1  6185
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