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Theorem alrot3 1390
Description: Theorem *11.21 in [WhiteheadRussell] p. 160. (Contributed by Andrew Salmon, 24-May-2011.)
Assertion
Ref Expression
alrot3 (∀𝑥𝑦𝑧𝜑 ↔ ∀𝑦𝑧𝑥𝜑)

Proof of Theorem alrot3
StepHypRef Expression
1 alcom 1383 . 2 (∀𝑥𝑦𝑧𝜑 ↔ ∀𝑦𝑥𝑧𝜑)
2 alcom 1383 . . 3 (∀𝑥𝑧𝜑 ↔ ∀𝑧𝑥𝜑)
32albii 1375 . 2 (∀𝑦𝑥𝑧𝜑 ↔ ∀𝑦𝑧𝑥𝜑)
41, 3bitri 177 1 (∀𝑥𝑦𝑧𝜑 ↔ ∀𝑦𝑧𝑥𝜑)
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:  alrot4  1391  raliunxp  4505  dff13  5435
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