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Theorem ax10lem4 1941
 Description: Lemma for ax10 1944. 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 1936 . . . . . 6
2 equequ1 1684 . . . . . . . 8
32dvelimv 1939 . . . . . . 7
4 hba1 1786 . . . . . . . . 9
5 equequ2 1686 . . . . . . . . . 10
65sps 1754 . . . . . . . . 9
74, 6albidh 1590 . . . . . . . 8
87biimprd 214 . . . . . . 7
93, 8syl6 29 . . . . . 6
101, 9syl7 63 . . . . 5
1110spsd 1755 . . . 4
1211pm2.43d 44 . . 3
1312com12 27 . 2
1413pm2.18d 103 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wi 4   wb 176  wal 1540 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925 This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545 This theorem is referenced by:  ax10lem5  1942
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