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Theorem rspc2ev 2963
 Description: 2-variable restricted existential specialization, using implicit substitution. (Contributed by NM, 16-Oct-1999.)
Hypotheses
Ref Expression
rspc2v.1
rspc2v.2
Assertion
Ref Expression
rspc2ev
Distinct variable groups:   ,,   ,   ,   ,,   ,   ,
Allowed substitution hints:   (,)   ()   ()   ()   ()

Proof of Theorem rspc2ev
StepHypRef Expression
1 rspc2v.2 . . . . 5
21rspcev 2955 . . . 4
32anim2i 552 . . 3
433impb 1147 . 2
5 rspc2v.1 . . . 4
65rexbidv 2635 . . 3
76rspcev 2955 . 2
84, 7syl 15 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 176   wa 358   w3a 934   wceq 1642   wcel 1710  wrex 2615 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-rex 2620  df-v 2861 This theorem is referenced by:  rspc3ev  2965  eladdci  4399  rspceov  5556  nclec  6195  ltcpw1pwg  6202  nc0le1  6216  nclenc  6222  ce2le  6233  tlenc1c  6240
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