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Theorem bj-hbaeb 34039
Description: Biconditional version of hbae 2445. (Contributed by BJ, 6-Oct-2018.) (Proof modification is discouraged.)
Assertion
Ref Expression
bj-hbaeb (∀𝑥 𝑥 = 𝑦 ↔ ∀𝑧𝑥 𝑥 = 𝑦)

Proof of Theorem bj-hbaeb
StepHypRef Expression
1 bj-hbaeb2 34038 . 2 (∀𝑥 𝑥 = 𝑦 ↔ ∀𝑥𝑧 𝑥 = 𝑦)
2 alcom 2153 . 2 (∀𝑥𝑧 𝑥 = 𝑦 ↔ ∀𝑧𝑥 𝑥 = 𝑦)
31, 2bitri 276 1 (∀𝑥 𝑥 = 𝑦 ↔ ∀𝑧𝑥 𝑥 = 𝑦)
Colors of variables: wff setvar class
Syntax hints:  wb 207  wal 1526
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1787  ax-4 1801  ax-5 1902  ax-6 1961  ax-7 2006  ax-10 2136  ax-11 2151  ax-12 2167  ax-13 2381
This theorem depends on definitions:  df-bi 208  df-an 397  df-or 842  df-tru 1531  df-ex 1772  df-nf 1776
This theorem is referenced by: (None)
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