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Theorem exrot4 1622
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 1620 . . 3 (∃𝑦𝑧𝑤𝜑 ↔ ∃𝑤𝑧𝑦𝜑)
21exbii 1537 . 2 (∃𝑥𝑦𝑧𝑤𝜑 ↔ ∃𝑥𝑤𝑧𝑦𝜑)
3 excom13 1620 . 2 (∃𝑥𝑤𝑧𝑦𝜑 ↔ ∃𝑧𝑤𝑥𝑦𝜑)
42, 3bitri 182 1 (∃𝑥𝑦𝑧𝑤𝜑 ↔ ∃𝑧𝑤𝑥𝑦𝜑)
Colors of variables: wff set class
Syntax hints:  wb 103  wex 1422
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-4 1441  ax-ial 1468
This theorem depends on definitions:  df-bi 115
This theorem is referenced by:  ee8anv  1853  elvvv  4450  dfoprab2  5605  xpassen  6397  enq0sym  6761
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