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Theorem alrot4 1447
Description: Rotate 4 universal quantifiers twice. (Contributed by NM, 2-Feb-2005.) (Proof shortened by Wolf Lammen, 28-Jun-2014.)
Assertion
Ref Expression
alrot4 (∀𝑥𝑦𝑧𝑤𝜑 ↔ ∀𝑧𝑤𝑥𝑦𝜑)

Proof of Theorem alrot4
StepHypRef Expression
1 alrot3 1446 . . 3 (∀𝑦𝑧𝑤𝜑 ↔ ∀𝑧𝑤𝑦𝜑)
21albii 1431 . 2 (∀𝑥𝑦𝑧𝑤𝜑 ↔ ∀𝑥𝑧𝑤𝑦𝜑)
3 alcom 1439 . 2 (∀𝑥𝑧𝑤𝑦𝜑 ↔ ∀𝑧𝑥𝑤𝑦𝜑)
4 alcom 1439 . . 3 (∀𝑥𝑤𝑦𝜑 ↔ ∀𝑤𝑥𝑦𝜑)
54albii 1431 . 2 (∀𝑧𝑥𝑤𝑦𝜑 ↔ ∀𝑧𝑤𝑥𝑦𝜑)
62, 3, 53bitri 205 1 (∀𝑥𝑦𝑧𝑤𝜑 ↔ ∀𝑧𝑤𝑥𝑦𝜑)
Colors of variables: wff set class
Syntax hints:  wb 104  wal 1314
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1408  ax-7 1409  ax-gen 1410
This theorem depends on definitions:  df-bi 116
This theorem is referenced by:  fun11  5160
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