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Theorem equcomiv 2002
Description: Weaker form of equcomi 2005 with a disjoint variable condition on 𝑥, 𝑦. This is an intermediate step and equcomi 2005 is fully recovered later. (Contributed by BJ, 7-Dec-2020.)
Assertion
Ref Expression
equcomiv (𝑥 = 𝑦𝑦 = 𝑥)
Distinct variable group:   𝑥,𝑦

Proof of Theorem equcomiv
StepHypRef Expression
1 equid 2000 . 2 𝑥 = 𝑥
2 ax7v2 1999 . 2 (𝑥 = 𝑦 → (𝑥 = 𝑥𝑦 = 𝑥))
31, 2mpi 20 1 (𝑥 = 𝑦𝑦 = 𝑥)
Colors of variables: wff setvar class
Syntax hints:  wi 4
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1781  ax-4 1795  ax-5 1892  ax-6 1951  ax-7 1996
This theorem depends on definitions:  df-bi 208  df-ex 1766
This theorem is referenced by:  ax6evr  2003
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