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Theorem r19.29vva 2473
 Description: A commonly used pattern based on r19.29 2467, version with two restricted quantifiers. (Contributed by Thierry Arnoux, 26-Nov-2017.)
Hypotheses
Ref Expression
r19.29vva.1
r19.29vva.2
Assertion
Ref Expression
r19.29vva
Distinct variable groups:   ,   ,,   ,,
Allowed substitution hints:   (,)   ()   (,)

Proof of Theorem r19.29vva
StepHypRef Expression
1 r19.29vva.1 . . . . . 6
21ex 112 . . . . 5
32ralrimiva 2409 . . . 4
43ralrimiva 2409 . . 3
5 r19.29vva.2 . . 3
64, 5r19.29d2r 2472 . 2
7 pm3.35 333 . . . . 5
87ancoms 259 . . . 4
98rexlimivw 2446 . . 3
109rexlimivw 2446 . 2
116, 10syl 14 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 101   wcel 1409  wral 2323  wrex 2324 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-5 1352  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-4 1416  ax-17 1435  ax-ial 1443  ax-i5r 1444 This theorem depends on definitions:  df-bi 114  df-nf 1366  df-ral 2328  df-rex 2329 This theorem is referenced by: (None)
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