Mathbox for Thierry Arnoux < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  cbvdisjf Structured version   Unicode version

Theorem cbvdisjf 24007
 Description: Change bound variables in a disjoint collection. (Contributed by Thierry Arnoux, 6-Apr-2017.)
Hypotheses
Ref Expression
cbvdisjf.1
cbvdisjf.2
cbvdisjf.3
cbvdisjf.4
Assertion
Ref Expression
cbvdisjf Disj Disj
Distinct variable groups:   ,   ,
Allowed substitution hints:   ()   (,)   (,)

Proof of Theorem cbvdisjf
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 nfv 1629 . . . . . 6
2 cbvdisjf.2 . . . . . . 7
32nfcri 2565 . . . . . 6
41, 3nfan 1846 . . . . 5
5 cbvdisjf.1 . . . . . . 7
65nfcri 2565 . . . . . 6
7 cbvdisjf.3 . . . . . . 7
87nfcri 2565 . . . . . 6
96, 8nfan 1846 . . . . 5
10 eleq1 2495 . . . . . 6
11 cbvdisjf.4 . . . . . . 7
1211eleq2d 2502 . . . . . 6
1310, 12anbi12d 692 . . . . 5
144, 9, 13cbvmo 2317 . . . 4
15 df-rmo 2705 . . . 4
16 df-rmo 2705 . . . 4
1714, 15, 163bitr4i 269 . . 3
1817albii 1575 . 2
19 df-disj 4175 . 2 Disj
20 df-disj 4175 . 2 Disj
2118, 19, 203bitr4i 269 1 Disj Disj
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wa 359  wal 1549   wceq 1652   wcel 1725  wmo 2281  wnfc 2558  wrmo 2700  Disj wdisj 4174 This theorem is referenced by:  disjorsf  24014 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-eu 2284  df-mo 2285  df-cleq 2428  df-clel 2431  df-nfc 2560  df-rmo 2705  df-disj 4175
 Copyright terms: Public domain W3C validator