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Theorem ax10-16 2266
 Description: This theorem shows that, given ax-16 2220, we can derive a version of ax-10 2216. However, it is weaker than ax-10 2216 because it has a distinct variable requirement. (Contributed by Andrew Salmon, 27-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
ax10-16
Distinct variable group:   ,

Proof of Theorem ax10-16
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 ax-16 2220 . . . 4
21alrimiv 1641 . . 3
32a5i-o 2226 . 2
4 equequ1 1696 . . . . . 6
54cbvalv 1984 . . . . . . 7
65a1i 11 . . . . . 6
74, 6imbi12d 312 . . . . 5
87albidv 1635 . . . 4
98cbvalv 1984 . . 3
109biimpi 187 . 2
11 nfa1-o 2242 . . . . . . 7
121119.23 1819 . . . . . 6
1312albii 1575 . . . . 5
14 a9ev 1668 . . . . . . . 8
15 pm2.27 37 . . . . . . . 8
1614, 15ax-mp 8 . . . . . . 7
1716alimi 1568 . . . . . 6
18 equequ2 1698 . . . . . . . . 9
1918spv 1965 . . . . . . . 8
2019sps-o 2235 . . . . . . 7
2120a7s 1750 . . . . . 6
2217, 21syl 16 . . . . 5
2313, 22sylbi 188 . . . 4
2423a7s 1750 . . 3
2524a5i-o 2226 . 2
263, 10, 253syl 19 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177  wal 1549  wex 1550 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-4 2211  ax-5o 2212  ax-6o 2213  ax-16 2220 This theorem depends on definitions:  df-bi 178  df-an 361  df-ex 1551  df-nf 1554
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