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Theorem rexlimdvv 2433
 Description: Inference from Theorem 19.23 of [Margaris] p. 90. (Restricted quantifier version.) (Contributed by NM, 22-Jul-2004.)
Hypothesis
Ref Expression
rexlimdvv.1 (φ → ((x A y B) → (ψχ)))
Assertion
Ref Expression
rexlimdvv (φ → (x A y B ψχ))
Distinct variable groups:   x,y,φ   χ,x,y   y,A
Allowed substitution hints:   ψ(x,y)   A(x)   B(x,y)

Proof of Theorem rexlimdvv
StepHypRef Expression
1 rexlimdvv.1 . . . 4 (φ → ((x A y B) → (ψχ)))
21expdimp 246 . . 3 ((φ x A) → (y B → (ψχ)))
32rexlimdv 2426 . 2 ((φ x A) → (y B ψχ))
43rexlimdva 2427 1 (φ → (x A y B ψχ))
 Colors of variables: wff set class Syntax hints:   → wi 4   ∧ wa 97   ∈ wcel 1390  ∃wrex 2301 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1333  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-4 1397  ax-17 1416  ax-ial 1424  ax-i5r 1425 This theorem depends on definitions:  df-bi 110  df-nf 1347  df-ral 2305  df-rex 2306 This theorem is referenced by:  rexlimdvva  2434  f1oiso2  5409  xpdom2  6241  genpcdl  6501  genpcuu  6502  distrlem1prl  6557  distrlem1pru  6558  distrlem5prl  6561  distrlem5pru  6562  recexprlemss1l  6606  recexprlemss1u  6607  qaddcl  8326  qmulcl  8328
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