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Theorem equcomi-o 1823
Description: Commutative law for equality. Lemma 7 of [Tarski] p. 69. Version of equcomi 1822 not requiring ax-17 1628. (Contributed by NM, 5-Aug-1993.)
Assertion
Ref Expression
equcomi-o  |-  ( x  =  y  ->  y  =  x )

Proof of Theorem equcomi-o
StepHypRef Expression
1 equid 1818 . 2  |-  x  =  x
2 ax-8 1623 . 2  |-  ( x  =  y  ->  (
x  =  x  -> 
y  =  x ) )
31, 2mpi 18 1  |-  ( x  =  y  ->  y  =  x )
Colors of variables: wff set class
Syntax hints:    -> wi 6
This theorem is referenced by:  alequcom-o  1838
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-6 1534  ax-gen 1536  ax-8 1623  ax-12o 1664  ax-9 1684  ax-4 1692
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