Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  csbeq2d Structured version   Visualization version   Unicode version

Theorem csbeq2d 3784
 Description: Formula-building deduction rule for class substitution. (Contributed by NM, 22-Nov-2005.) (Revised by Mario Carneiro, 1-Sep-2015.)
Hypotheses
Ref Expression
csbeq2d.1
csbeq2d.2
Assertion
Ref Expression
csbeq2d

Proof of Theorem csbeq2d
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 csbeq2d.1 . . . 4
2 csbeq2d.2 . . . . 5
32eleq2d 2534 . . . 4
41, 3sbcbid 3309 . . 3
54abbidv 2589 . 2
6 df-csb 3350 . 2
7 df-csb 3350 . 2
85, 6, 73eqtr4g 2530 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wceq 1452  wnf 1675   wcel 1904  cab 2457  wsbc 3255  csb 3349 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1677  ax-4 1690  ax-5 1766  ax-6 1813  ax-7 1859  ax-10 1932  ax-11 1937  ax-12 1950  ax-13 2104  ax-ext 2451 This theorem depends on definitions:  df-bi 190  df-an 378  df-tru 1455  df-ex 1672  df-nf 1676  df-sb 1806  df-clab 2458  df-cleq 2464  df-clel 2467  df-sbc 3256  df-csb 3350 This theorem is referenced by:  csbeq2dv  3785  poimirlem26  32030
 Copyright terms: Public domain W3C validator