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Theorem sbceq2g 3158
Description: Move proper substitution to second argument of an equality. (Contributed by NM, 30-Nov-2005.)
Assertion
Ref Expression
sbceq2g  [.  ].
Distinct variable group:   ,
Allowed substitution hints:   ()   ()   ()

Proof of Theorem sbceq2g
StepHypRef Expression
1 sbceqg 3152 . 2  [.  ].
2 csbconstg 3150 . . 3
32eqeq1d 2361 . 2
41, 3bitrd 244 1  [.  ].
Colors of variables: wff setvar class
Syntax hints:   wi 4   wb 176   wceq 1642   wcel 1710   [.wsbc 3046  csb 3136
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  ax-ext 2334
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-v 2861  df-sbc 3047  df-csb 3137
This theorem is referenced by:  csbsng  3785  eqerlem  5960
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