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Theorem sbeqal2i 27268
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 27267 . 2  |-  y  =  z
32eqcomi 2391 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 1552  ax-5 1563  ax-17 1623  ax-9 1661  ax-8 1682  ax-6 1736  ax-7 1741  ax-11 1753  ax-12 1939  ax-ext 2368
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-cleq 2380
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