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

Step	Hyp	Ref	Expression
1		equid 1863	. 2 |- x = x
2		ax7v2 1862	. 2 |- ( x = y -> ( x = x -> y = x ) )
3	1, 2	mpi 20	1 |- ( x = y -> y = x )

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