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Theorem alrot3 2161
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 2160 . 2 (∀𝑥𝑦𝑧𝜑 ↔ ∀𝑦𝑥𝑧𝜑)
2 alcom 2160 . . 3 (∀𝑥𝑧𝜑 ↔ ∀𝑧𝑥𝜑)
32albii 1826 . 2 (∀𝑦𝑥𝑧𝜑 ↔ ∀𝑦𝑧𝑥𝜑)
41, 3bitri 274 1 (∀𝑥𝑦𝑧𝜑 ↔ ∀𝑦𝑧𝑥𝜑)
Colors of variables: wff setvar class
Syntax hints:  wb 205  wal 1540
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1802  ax-4 1816  ax-11 2158
This theorem depends on definitions:  df-bi 206
This theorem is referenced by:  alrot4  2162  nfnid  5302  raliunxp  5747  dff13  7125  cosscnvssid3  36590  undmrnresiss  41182
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