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Theorem alrot3 1462
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 1455 . 2 (∀𝑥𝑦𝑧𝜑 ↔ ∀𝑦𝑥𝑧𝜑)
2 alcom 1455 . . 3 (∀𝑥𝑧𝜑 ↔ ∀𝑧𝑥𝜑)
32albii 1447 . 2 (∀𝑦𝑥𝑧𝜑 ↔ ∀𝑦𝑧𝑥𝜑)
41, 3bitri 183 1 (∀𝑥𝑦𝑧𝜑 ↔ ∀𝑦𝑧𝑥𝜑)
Colors of variables: wff set class
Syntax hints:  wb 104  wal 1330
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 1424  ax-7 1425  ax-gen 1426
This theorem depends on definitions:  df-bi 116
This theorem is referenced by:  alrot4  1463  raliunxp  4687  dff13  5676
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