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Theorem rexrot4 2774
Description: Rotate existential restricted quantifiers twice. (Contributed by NM, 8-Apr-2015.)
Ref Expression
rexrot4 (x A y B z C w D φz C w D x A y B φ)
Distinct variable groups:   z,w,A   w,B,z   x,w,y,C   x,z,D,y
Allowed substitution hints:   φ(x,y,z,w)   A(x,y)   B(x,y)   C(z)   D(w)

Proof of Theorem rexrot4
StepHypRef Expression
1 rexcom13 2773 . . 3 (y B z C w D φw D z C y B φ)
21rexbii 2639 . 2 (x A y B z C w D φx A w D z C y B φ)
3 rexcom13 2773 . 2 (x A w D z C y B φz C w D x A y B φ)
42, 3bitri 240 1 (x A y B z C w D φz C w D x A y B φ)
Colors of variables: wff setvar class
Syntax hints:  wb 176  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-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-cleq 2346  df-clel 2349  df-nfc 2478  df-rex 2620
This theorem is referenced by: (None)
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