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Theorem equequ2OLD 1952
Description: Obsolete proof of equequ2 1950 as of 12-Apr-2021. (Contributed by NM, 21-Jun-1993.) (Proof shortened by Wolf Lammen, 4-Aug-2017.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
equequ2OLD (𝑥 = 𝑦 → (𝑧 = 𝑥𝑧 = 𝑦))

Proof of Theorem equequ2OLD
StepHypRef Expression
1 equequ1 1949 . 2 (𝑥 = 𝑦 → (𝑥 = 𝑧𝑦 = 𝑧))
2 equcom 1942 . 2 (𝑥 = 𝑧𝑧 = 𝑥)
3 equcom 1942 . 2 (𝑦 = 𝑧𝑧 = 𝑦)
41, 2, 33bitr3g 302 1 (𝑥 = 𝑦 → (𝑧 = 𝑥𝑧 = 𝑦))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 196
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1719  ax-4 1734  ax-5 1836  ax-6 1885  ax-7 1932
This theorem depends on definitions:  df-bi 197  df-an 386  df-ex 1702
This theorem is referenced by: (None)
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