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Theorem alrot4 2036
Description: Rotate four universal quantifiers twice. (Contributed by NM, 2-Feb-2005.) (Proof shortened by Fan Zheng, 6-Jun-2016.)
Assertion
Ref Expression
alrot4 (∀𝑥𝑦𝑧𝑤𝜑 ↔ ∀𝑧𝑤𝑥𝑦𝜑)

Proof of Theorem alrot4
StepHypRef Expression
1 alrot3 2035 . . 3 (∀𝑦𝑧𝑤𝜑 ↔ ∀𝑧𝑤𝑦𝜑)
21albii 1744 . 2 (∀𝑥𝑦𝑧𝑤𝜑 ↔ ∀𝑥𝑧𝑤𝑦𝜑)
3 alrot3 2035 . 2 (∀𝑥𝑧𝑤𝑦𝜑 ↔ ∀𝑧𝑤𝑥𝑦𝜑)
42, 3bitri 264 1 (∀𝑥𝑦𝑧𝑤𝜑 ↔ ∀𝑧𝑤𝑥𝑦𝜑)
Colors of variables: wff setvar class
Syntax hints:  wb 196  wal 1478
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
This theorem is referenced by:  2mo  2550  fun11  5926
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