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Theorem exrot3 2165
Description: Rotate existential quantifiers. (Contributed by NM, 17-Mar-1995.)
Assertion
Ref Expression
exrot3 (∃𝑥𝑦𝑧𝜑 ↔ ∃𝑦𝑧𝑥𝜑)

Proof of Theorem exrot3
StepHypRef Expression
1 excom13 2164 . 2 (∃𝑥𝑦𝑧𝜑 ↔ ∃𝑧𝑦𝑥𝜑)
2 excom 2162 . 2 (∃𝑧𝑦𝑥𝜑 ↔ ∃𝑦𝑧𝑥𝜑)
31, 2bitri 274 1 (∃𝑥𝑦𝑧𝜑 ↔ ∃𝑦𝑧𝑥𝜑)
Colors of variables: wff setvar class
Syntax hints:  wb 205  wex 1782
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-11 2154
This theorem depends on definitions:  df-bi 206  df-ex 1783
This theorem is referenced by:  opabn0  5466  dmoprab  7376  rnoprab  7378  xpassen  8853  cnvoprabOLD  31055  elima4  33750  brimg  34239  ellines  34454  rnxrn  36524  fundcmpsurinj  44861
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