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Theorem ax6e2eq 36918
 Description: Alternate form of ax6e 2093 for non-distinct , and . ax6e2eq 36918 is derived from ax6e2eqVD 37298. (Contributed by Alan Sare, 25-Mar-2014.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
ax6e2eq
Distinct variable groups:   ,   ,   ,   ,

Proof of Theorem ax6e2eq
StepHypRef Expression
1 ax6ev 1806 . . . . . . 7
2 hbae 2148 . . . . . . . 8
3 ax7 1859 . . . . . . . . . 10
43sps 1942 . . . . . . . . 9
54ancld 556 . . . . . . . 8
62, 5eximdh 1723 . . . . . . 7
71, 6mpi 20 . . . . . 6
87axc4i 1979 . . . . 5
9 axc11 2147 . . . . 5
108, 9mpd 15 . . . 4
11 19.2 1808 . . . 4
1210, 11syl 17 . . 3
13 excomim 1928 . . 3
1412, 13syl 17 . 2
15 equtrr 1865 . . . 4
1615anim2d 568 . . 3
17162eximdv 1765 . 2
1814, 17syl5com 31 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wa 371  wal 1441  wex 1662 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1668  ax-4 1681  ax-5 1757  ax-6 1804  ax-7 1850  ax-10 1914  ax-11 1919  ax-12 1932  ax-13 2090 This theorem depends on definitions:  df-bi 189  df-an 373  df-ex 1663  df-nf 1667 This theorem is referenced by:  ax6e2ndeq  36920  ax6e2ndeqVD  37300  ax6e2ndeqALT  37322
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