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Theorem equcomiv 1866
Description: Weaker form of equcomi 1869 with a dv condition on  x ,  y. This is an intermediate step and equcomi 1869 is fully recovered later. (Contributed by BJ, 7-Dec-2020.)
Assertion
Ref Expression
equcomiv  |-  ( x  =  y  ->  y  =  x )
Distinct variable group:    x, y

Proof of Theorem equcomiv
StepHypRef Expression
1 equid 1863 . 2  |-  x  =  x
2 ax7v2 1862 . 2  |-  ( x  =  y  ->  (
x  =  x  -> 
y  =  x ) )
31, 2mpi 20 1  |-  ( x  =  y  ->  y  =  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 1677  ax-4 1690  ax-5 1766  ax-6 1813  ax-7 1859
This theorem depends on definitions:  df-bi 190  df-ex 1672
This theorem is referenced by:  ax6evr  1867  ax8  1910  ax9  1917
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