ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  exrot4 GIF version

Theorem exrot4 1684
Description: Rotate existential quantifiers twice. (Contributed by NM, 9-Mar-1995.)
Assertion
Ref Expression
exrot4 (∃𝑥𝑦𝑧𝑤𝜑 ↔ ∃𝑧𝑤𝑥𝑦𝜑)

Proof of Theorem exrot4
StepHypRef Expression
1 excom13 1682 . . 3 (∃𝑦𝑧𝑤𝜑 ↔ ∃𝑤𝑧𝑦𝜑)
21exbii 1598 . 2 (∃𝑥𝑦𝑧𝑤𝜑 ↔ ∃𝑥𝑤𝑧𝑦𝜑)
3 excom13 1682 . 2 (∃𝑥𝑤𝑧𝑦𝜑 ↔ ∃𝑧𝑤𝑥𝑦𝜑)
42, 3bitri 183 1 (∃𝑥𝑦𝑧𝑤𝜑 ↔ ∃𝑧𝑤𝑥𝑦𝜑)
Colors of variables: wff set class
Syntax hints:  wb 104  wex 1485
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1440  ax-7 1441  ax-gen 1442  ax-ie1 1486  ax-ie2 1487  ax-4 1503  ax-ial 1527
This theorem depends on definitions:  df-bi 116
This theorem is referenced by:  ee8anv  1928  elvvv  4674  dfoprab2  5900  xpassen  6808  enq0sym  7394
  Copyright terms: Public domain W3C validator