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Theorem bj-hbaeb 36802
Description: Biconditional version of hbae 2434. (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 36801 . 2 (∀𝑥 𝑥 = 𝑦 ↔ ∀𝑥𝑧 𝑥 = 𝑦)
2 alcom 2157 . 2 (∀𝑥𝑧 𝑥 = 𝑦 ↔ ∀𝑧𝑥 𝑥 = 𝑦)
31, 2bitri 275 1 (∀𝑥 𝑥 = 𝑦 ↔ ∀𝑧𝑥 𝑥 = 𝑦)
Colors of variables: wff setvar class
Syntax hints:  wb 206  wal 1535
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1792  ax-4 1806  ax-5 1908  ax-6 1965  ax-7 2005  ax-10 2139  ax-11 2155  ax-12 2175  ax-13 2375
This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-tru 1540  df-ex 1777  df-nf 1781
This theorem is referenced by: (None)
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