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Theorem sbidm 2085
Description: An idempotent law for substitution. (Contributed by NM, 30-Jun-1994.) (Proof shortened by Andrew Salmon, 25-May-2011.)
Assertion
Ref Expression
sbidm

Proof of Theorem sbidm
StepHypRef Expression
1 equsb2 2035 . . 3
2 sbequ12r 1920 . . . 4
32sbimi 1652 . . 3
41, 3ax-mp 5 . 2
5 sbbi 2071 . 2
64, 5mpbi 199 1
Colors of variables: wff setvar class
Syntax hints:   wb 176  wsb 1648
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925
This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649
This theorem is referenced by: (None)
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