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Theorem ralimdaa 2582
 Description: Deduction quantifying both antecedent and consequent, based on Theorem 19.20 of [Margaris] p. 90. (Contributed by NM, 22-Sep-2003.)
Hypotheses
Ref Expression
ralimdaa.1
ralimdaa.2
Assertion
Ref Expression
ralimdaa

Proof of Theorem ralimdaa
StepHypRef Expression
1 ralimdaa.1 . . 3
2 ralimdaa.2 . . . . 5
32ex 425 . . . 4
43a2d 25 . . 3
51, 4alimd 1705 . 2
6 df-ral 2513 . 2
7 df-ral 2513 . 2
85, 6, 73imtr4g 263 1
 Colors of variables: wff set class Syntax hints:   wi 6   wa 360  wal 1532  wnf 1539   wcel 1621  wral 2509 This theorem is referenced by:  ralimdva  2583  eltsk2g  8253  ptcnplem  17147 This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-gen 1536  ax-4 1692 This theorem depends on definitions:  df-bi 179  df-an 362  df-nf 1540  df-ral 2513
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