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Theorem a9e2eq 28581
 Description: Alternate form of a9e 1952 for non-distinct , and . a9e2eq 28581 is derived from a9e2eqVD 28956. (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 1668 . . . . . . 7
2 hbae 2040 . . . . . . . 8
3 ax-8 1687 . . . . . . . . . 10
43sps 1770 . . . . . . . . 9
54ancld 537 . . . . . . . 8
62, 5eximdh 1598 . . . . . . 7
71, 6mpi 17 . . . . . 6
87a5i 1807 . . . . 5
9 ax10o 2038 . . . . 5
108, 9mpd 15 . . . 4
11 19.2 1671 . . . 4
1210, 11syl 16 . . 3
13 excomim 1757 . . 3
1412, 13syl 16 . 2
15 equtrr 1695 . . . 4
1615anim2d 549 . . 3
17162eximdv 1634 . 2
1814, 17syl5com 28 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 359  wal 1549  wex 1550 This theorem is referenced by:  a9e2ndeq  28583  a9e2ndeqVD  28958  a9e2ndeqALT  28980 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 This theorem depends on definitions:  df-bi 178  df-an 361  df-ex 1551  df-nf 1554
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