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Theorem exrot4 2043
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 2041 . . 3 (∃𝑦𝑧𝑤𝜑 ↔ ∃𝑤𝑧𝑦𝜑)
21exbii 1771 . 2 (∃𝑥𝑦𝑧𝑤𝜑 ↔ ∃𝑥𝑤𝑧𝑦𝜑)
3 excom13 2041 . 2 (∃𝑥𝑤𝑧𝑦𝜑 ↔ ∃𝑧𝑤𝑥𝑦𝜑)
42, 3bitri 264 1 (∃𝑥𝑦𝑧𝑤𝜑 ↔ ∃𝑧𝑤𝑥𝑦𝜑)
Colors of variables: wff setvar class
Syntax hints:  wb 196  wex 1701
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1719  ax-4 1734  ax-11 2031
This theorem depends on definitions:  df-bi 197  df-ex 1702
This theorem is referenced by:  elvvv  5141  dfoprab2  6657  xpassen  8001  5oalem7  28380  elfuns  31685
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