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Theorem alrot4 1391
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 1390 . . 3 (∀𝑦𝑧𝑤𝜑 ↔ ∀𝑧𝑤𝑦𝜑)
21albii 1375 . 2 (∀𝑥𝑦𝑧𝑤𝜑 ↔ ∀𝑥𝑧𝑤𝑦𝜑)
3 alcom 1383 . 2 (∀𝑥𝑧𝑤𝑦𝜑 ↔ ∀𝑧𝑥𝑤𝑦𝜑)
4 alcom 1383 . . 3 (∀𝑥𝑤𝑦𝜑 ↔ ∀𝑤𝑥𝑦𝜑)
54albii 1375 . 2 (∀𝑧𝑥𝑤𝑦𝜑 ↔ ∀𝑧𝑤𝑥𝑦𝜑)
62, 3, 53bitri 199 1 (∀𝑥𝑦𝑧𝑤𝜑 ↔ ∀𝑧𝑤𝑥𝑦𝜑)
Colors of variables: wff set class
Syntax hints:  wb 102  wal 1257
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
This theorem depends on definitions:  df-bi 114
This theorem is referenced by:  fun11  4994
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