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Theorem a16g 1898
 Description: Generalization of ax16 1998. (Contributed by NM, 25-Jul-2015.)
Assertion
Ref Expression
a16g
Distinct variable group:   ,
Allowed substitution hints:   (,,)

Proof of Theorem a16g
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 a9ev 1646 . 2
2 ax10lem5 1895 . 2
3 hbn1 1716 . . . . 5
4 pm2.21 100 . . . . 5
53, 4alrimih 1555 . . . 4
6 ax-17 1606 . . . . 5
7 ax-1 5 . . . . 5
86, 7alrimih 1555 . . . 4
95, 8ja 153 . . 3
10 ax10lem5 1895 . . . 4
11 equcomi 1664 . . . . . . 7
12 ax-17 1606 . . . . . . 7
13 ax-11 1727 . . . . . . 7
1411, 12, 13syl2im 34 . . . . . 6
15 ax-5 1547 . . . . . 6
1614, 15syl6 29 . . . . 5
1716com23 72 . . . 4
1810, 17syl5 28 . . 3
199, 18exlimih 1741 . 2
201, 2, 19mpsyl 59 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4  wal 1530  wex 1531 This theorem is referenced by:  ax16  1998  a16gb  2003  a16nf  2004 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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