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Theorem exrot4 1597
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 1595 . . 3 (∃𝑦𝑧𝑤𝜑 ↔ ∃𝑤𝑧𝑦𝜑)
21exbii 1512 . 2 (∃𝑥𝑦𝑧𝑤𝜑 ↔ ∃𝑥𝑤𝑧𝑦𝜑)
3 excom13 1595 . 2 (∃𝑥𝑤𝑧𝑦𝜑 ↔ ∃𝑧𝑤𝑥𝑦𝜑)
42, 3bitri 177 1 (∃𝑥𝑦𝑧𝑤𝜑 ↔ ∃𝑧𝑤𝑥𝑦𝜑)
Colors of variables: wff set class
Syntax hints:  wb 102  wex 1397
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-4 1416  ax-ial 1443
This theorem depends on definitions:  df-bi 114
This theorem is referenced by:  ee8anv  1826  elvvv  4430  dfoprab2  5579  xpassen  6334  enq0sym  6587
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