New Foundations Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  NFE Home  >  Th. List  >  sbabel Unicode version

Theorem sbabel 2515
 Description: Theorem to move a substitution in and out of a class abstraction. (Contributed by NM, 27-Sep-2003.) (Revised by Mario Carneiro, 7-Oct-2016.)
Hypothesis
Ref Expression
sbabel.1
Assertion
Ref Expression
sbabel
Distinct variable groups:   ,   ,
Allowed substitution hints:   (,,)   (,,)

Proof of Theorem sbabel
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 sbex 2128 . . 3
2 sban 2069 . . . . 5
3 nfv 1619 . . . . . . . . . 10
43sbf 2026 . . . . . . . . 9
54sbrbis 2073 . . . . . . . 8
65sbalv 2129 . . . . . . 7
7 abeq2 2458 . . . . . . . 8
87sbbii 1653 . . . . . . 7
9 abeq2 2458 . . . . . . 7
106, 8, 93bitr4i 268 . . . . . 6
11 sbabel.1 . . . . . . . 8
1211nfcri 2483 . . . . . . 7
1312sbf 2026 . . . . . 6
1410, 13anbi12i 678 . . . . 5
152, 14bitri 240 . . . 4
1615exbii 1582 . . 3
171, 16bitri 240 . 2
18 df-clel 2349 . . 3
1918sbbii 1653 . 2
20 df-clel 2349 . 2
2117, 19, 203bitr4i 268 1
 Colors of variables: wff setvar class Syntax hints:   wb 176   wa 358  wal 1540  wex 1541   wceq 1642  wsb 1648   wcel 1710  cab 2339  wnfc 2476 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 This theorem is referenced by: (None)
 Copyright terms: Public domain W3C validator