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Theorem ax10lem4 1894
 Description: Lemma for ax10 1897. Change bound variable. (Contributed by NM, 8-Jul-2016.)
Assertion
Ref Expression
ax10lem4
Distinct variable groups:   ,   ,

Proof of Theorem ax10lem4
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 ax10lem1 1889 . . . . . 6
2 equequ1 1667 . . . . . . . 8
32dvelimv 1892 . . . . . . 7
4 hba1 1731 . . . . . . . . 9
5 equequ2 1669 . . . . . . . . . 10
65sps 1751 . . . . . . . . 9
74, 6albidh 1580 . . . . . . . 8
87biimprd 214 . . . . . . 7
93, 8syl6 29 . . . . . 6
101, 9syl7 63 . . . . 5
1110spsd 1752 . . . 4
1211pm2.43d 44 . . 3
1312com12 27 . 2
1413pm2.18d 103 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wb 176  wal 1530 This theorem is referenced by:  ax10lem5  1895 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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