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Theorem exrot3 2163
Description: Rotate existential quantifiers. (Contributed by NM, 17-Mar-1995.)
Assertion
Ref Expression
exrot3 (∃𝑥𝑦𝑧𝜑 ↔ ∃𝑦𝑧𝑥𝜑)

Proof of Theorem exrot3
StepHypRef Expression
1 excom13 2162 . 2 (∃𝑥𝑦𝑧𝜑 ↔ ∃𝑧𝑦𝑥𝜑)
2 excom 2160 . 2 (∃𝑧𝑦𝑥𝜑 ↔ ∃𝑦𝑧𝑥𝜑)
31, 2bitri 275 1 (∃𝑥𝑦𝑧𝜑 ↔ ∃𝑦𝑧𝑥𝜑)
Colors of variables: wff setvar class
Syntax hints:  wb 206  wex 1776
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1792  ax-4 1806  ax-11 2155
This theorem depends on definitions:  df-bi 207  df-ex 1777
This theorem is referenced by:  opabn0  5563  dmoprab  7535  rnoprab  7537  xpassen  9105  cnvoprabOLD  32738  elima4  35757  brimg  35919  ellines  36134  rnxrn  38380  fundcmpsurinj  47334
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