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Theorem ralimdv 2438
Description: Deduction quantifying both antecedent and consequent, based on Theorem 19.20 of [Margaris] p. 90. (Contributed by NM, 8-Oct-2003.)
Hypothesis
Ref Expression
ralimdv.1  |-  ( ph  ->  ( ps  ->  ch ) )
Assertion
Ref Expression
ralimdv  |-  ( ph  ->  ( A. x  e.  A  ps  ->  A. x  e.  A  ch )
)
Distinct variable group:    ph, x
Allowed substitution hints:    ps( x)    ch( x)    A( x)

Proof of Theorem ralimdv
StepHypRef Expression
1 ralimdv.1 . . 3  |-  ( ph  ->  ( ps  ->  ch ) )
21adantr 270 . 2  |-  ( (
ph  /\  x  e.  A )  ->  ( ps  ->  ch ) )
32ralimdva 2437 1  |-  ( ph  ->  ( A. x  e.  A  ps  ->  A. x  e.  A  ch )
)
Colors of variables: wff set class
Syntax hints:    -> wi 4    e. wcel 1436   A.wral 2355
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1379  ax-gen 1381  ax-4 1443  ax-17 1462
This theorem depends on definitions:  df-bi 115  df-nf 1393  df-ral 2360
This theorem is referenced by:  poss  4101  sess1  4140  sess2  4141  riinint  4664  dffo4  5412  dffo5  5413  isoini2  5561  rdgivallem  6102  iinerm  6318  xpf1o  6514  resqrexlemgt0  10352  cau3lem  10446  caubnd2  10449  climshftlemg  10588  climcau  10631  climcaucn  10635  serif0  10636  bezoutlemmain  10893
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