Mathbox for Scott Fenton < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  axextdist Structured version   Unicode version

Theorem axextdist 25427
 Description: ax-ext 2417 with distinctors instead of distinct variable restrictions. (Contributed by Scott Fenton, 13-Dec-2010.)
Assertion
Ref Expression
axextdist

Proof of Theorem axextdist
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 nfnae 2044 . . . 4
2 nfnae 2044 . . . 4
31, 2nfan 1846 . . 3
4 nfcvf 2594 . . . . . 6
54adantr 452 . . . . 5
65nfcrd 2585 . . . 4
7 nfcvf 2594 . . . . . 6
87adantl 453 . . . . 5
98nfcrd 2585 . . . 4
106, 9nfbid 1854 . . 3
11 elequ1 1728 . . . . 5
12 elequ1 1728 . . . . 5
1311, 12bibi12d 313 . . . 4
1413a1i 11 . . 3
153, 10, 14cbvald 1986 . 2
16 axext3 2419 . 2
1715, 16syl6bir 221 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wb 177   wa 359  wal 1549  wnfc 2559 This theorem is referenced by:  axext4dist  25428 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-13 1727  ax-14 1729  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417 This theorem depends on definitions:  df-bi 178  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-cleq 2429  df-clel 2432  df-nfc 2561
 Copyright terms: Public domain W3C validator