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Theorem alrot3 2188
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 2187 . 2 (∀𝑥𝑦𝑧𝜑 ↔ ∀𝑦𝑥𝑧𝜑)
2 alcom 2187 . . 3 (∀𝑥𝑧𝜑 ↔ ∀𝑧𝑥𝜑)
32albii 1896 . 2 (∀𝑦𝑥𝑧𝜑 ↔ ∀𝑦𝑧𝑥𝜑)
41, 3bitri 264 1 (∀𝑥𝑦𝑧𝜑 ↔ ∀𝑦𝑧𝑥𝜑)
Colors of variables: wff setvar class
Syntax hints:  wb 196  wal 1630
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1871  ax-4 1886  ax-11 2184
This theorem depends on definitions:  df-bi 197
This theorem is referenced by:  alrot4  2189  nfnid  5047  raliunxp  5418  dff13  6677  cosscnvssid3  34568  undmrnresiss  38431  ntrneikb  38913  ntrneixb  38914
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