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Theorem sbeqal2i 27702
Description: If  x  =  y implies  x  =  z, then we can infer  z  =  y. (Contributed by Andrew Salmon, 3-Jun-2011.)
Hypothesis
Ref Expression
sbeqal1i.1  |-  ( x  =  y  ->  x  =  z )
Assertion
Ref Expression
sbeqal2i  |-  z  =  y
Distinct variable group:    x, z

Proof of Theorem sbeqal2i
StepHypRef Expression
1 sbeqal1i.1 . . 3  |-  ( x  =  y  ->  x  =  z )
21sbeqal1i 27701 . 2  |-  y  =  z
32eqcomi 2300 1  |-  z  =  y
Colors of variables: wff set class
Syntax hints:    -> wi 4
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-cleq 2289
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