Mathbox for Alan Sare < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  a9e2eq Unicode version

Theorem a9e2eq 28622
 Description: Alternate form of a9e 1904 for non-distinct , and . a9e2eq 28622 is derived from a9e2eqVD 28999. (Contributed by Alan Sare, 25-Mar-2014.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
a9e2eq
Distinct variable groups:   ,   ,   ,   ,

Proof of Theorem a9e2eq
StepHypRef Expression
1 a9ev 1646 . . . . . . 7
2 hbae 1906 . . . . . . . 8
3 ax-8 1661 . . . . . . . . . 10
43sps 1751 . . . . . . . . 9
54ancld 536 . . . . . . . 8
62, 5eximdh 1578 . . . . . . 7
71, 6mpi 16 . . . . . 6
87a5i 1770 . . . . 5
9 ax10o 1905 . . . . 5
108, 9mpd 14 . . . 4
11 19.2 1648 . . . 4
1210, 11syl 15 . . 3
13 excomim 1797 . . 3
1412, 13syl 15 . 2
15 equtrr 1672 . . . 4
1615anim2d 548 . . 3
17162eximdv 1614 . 2
1814, 17syl5com 26 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 358  wal 1530  wex 1531 This theorem is referenced by:  a9e2ndeq  28624  a9e2ndeqVD  29001  a9e2ndeqALT  29024 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878 This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1310  df-ex 1532  df-nf 1535
 Copyright terms: Public domain W3C validator