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Theorem sbc4rexg 26189
 Description: Exchange a substitution with 4 existentials. (Contributed by Stefan O'Rear, 11-Oct-2014.)
Assertion
Ref Expression
sbc4rexg
Distinct variable groups:   ,   ,   ,   ,   ,   ,   ,   ,   ,   ,   ,   ,
Allowed substitution hints:   (,,,,)   ()   (,,,)   (,,,)   (,,,)   (,,,)   (,,,,)

Proof of Theorem sbc4rexg
StepHypRef Expression
1 elex 2872 . 2
2 sbc2rexg 26188 . . 3
3 sbc2rexg 26188 . . . 4
432rexbidv 2662 . . 3
52, 4bitrd 244 . 2
61, 5syl 15 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 176   wcel 1710  wrex 2620  cvv 2864  wsbc 3067 This theorem is referenced by:  6rexfrabdioph  26203  7rexfrabdioph  26204 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 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 1930  ax-ext 2339 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2345  df-cleq 2351  df-clel 2354  df-nfc 2483  df-ral 2624  df-rex 2625  df-v 2866  df-sbc 3068
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