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Theorem ax10lem18ALT 29746
 Description: Distinctor with bound variable change without using sp 1728, ax9 1902, or ax10 1897 but allowing ax9v 1645. Uses ax12o 1887. (Contributed by NM, 22-Jul-2015.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
ax10lem18ALT
Distinct variable groups:   ,   ,

Proof of Theorem ax10lem18ALT
StepHypRef Expression
1 sp 1728 . . 3
2 ax10lem1 1889 . . . 4
3 equcomi 1664 . . . . 5
4 ax10lem17ALT 29745 . . . . . 6
5 equcomi 1664 . . . . . . 7
65alimi 1549 . . . . . 6
74, 6syl6 29 . . . . 5
8 hba1 1731 . . . . . . 7
9 sp 1728 . . . . . . . 8
10 equequ2 1669 . . . . . . . 8
119, 10syl 15 . . . . . . 7
128, 11albidh 1580 . . . . . 6
1312biimprd 214 . . . . 5
143, 7, 13syl56 30 . . . 4
152, 14syl7 63 . . 3
161, 15syl5 28 . 2
1716pm2.43d 44 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wb 176  wal 1530 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-ex 1532
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