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Theorem reeanv 2778
 Description: Rearrange existential quantifiers. (Contributed by NM, 9-May-1999.)
Assertion
Ref Expression
reeanv (x A y B (φ ψ) ↔ (x A φ y B ψ))
Distinct variable groups:   φ,y   ψ,x   x,y   y,A   x,B
Allowed substitution hints:   φ(x)   ψ(y)   A(x)   B(y)

Proof of Theorem reeanv
StepHypRef Expression
1 nfv 1619 . 2 yφ
2 nfv 1619 . 2 xψ
31, 2reean 2777 1 (x A y B (φ ψ) ↔ (x A φ y B ψ))
 Colors of variables: wff setvar class Syntax hints:   ↔ wb 176   ∧ wa 358  ∃wrex 2615 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 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:  3reeanv  2779  2ralor  2780  ltfintr  4459  ncfinraise  4481  ncfinlower  4483  nnpw1ex  4484  tfin11  4493  nnpweq  4523  sfinltfin  4535  dfxp2  5113  xpassen  6057  peano4nc  6150  ncspw1eu  6159  sbth  6206  lectr  6211
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