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Theorem rspc2edv 24963
 Description: 2-variable restricted existential specialization, using implicit substitution. (rspc2ev 2892 with an antecedent.) (Contributed by FL, 2-Jul-2012.)
Hypotheses
Ref Expression
rspc2edv.1
rspc2edv.2
Assertion
Ref Expression
rspc2edv
Distinct variable groups:   ,,   ,   ,   ,,   ,   ,,   ,
Allowed substitution hints:   (,)   ()   ()   ()   ()

Proof of Theorem rspc2edv
StepHypRef Expression
1 rspc2edv.1 . . . . . . . 8
21anbi2d 684 . . . . . . 7
3 rspc2edv.2 . . . . . . . 8
43anbi2d 684 . . . . . . 7
52, 4rspc2ev 2892 . . . . . 6
6 simpr 447 . . . . . . . 8
76reximi 2650 . . . . . . 7
87reximi 2650 . . . . . 6
95, 8syl 15 . . . . 5
1093expia 1153 . . . 4
1110exp4b 590 . . 3
1211com3r 73 . 2
13123imp 1145 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 176   wa 358   w3a 934   wceq 1623   wcel 1684  wrex 2544 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-ral 2548  df-rex 2549  df-v 2790
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