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Theorem a16gNEW7 29473
 Description: Generalization of ax16 2129. (Contributed by NM, 25-Jul-2015.)
Assertion
Ref Expression
a16gNEW7
Distinct variable group:   ,
Allowed substitution hints:   (,,)

Proof of Theorem a16gNEW7
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 a9ev 1668 . 2
2 ax10lem5NEW7 29399 . 2
3 hbn1 1745 . . . . 5
4 pm2.21 102 . . . . 5
53, 4alrimih 1574 . . . 4
6 ax-17 1626 . . . . 5
7 ax-1 5 . . . . 5
86, 7alrimih 1574 . . . 4
95, 8ja 155 . . 3
10 ax10lem5NEW7 29399 . . . 4
11 equcomi 1691 . . . . . . 7
12 ax-17 1626 . . . . . . 7
13 ax-11 1761 . . . . . . 7
1411, 12, 13syl2im 36 . . . . . 6
15 ax-5 1566 . . . . . 6
1614, 15syl6 31 . . . . 5
1716com23 74 . . . 4
1810, 17syl5 30 . . 3
199, 18exlimih 1822 . 2
201, 2, 19mpsyl 61 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4  wal 1549  wex 1550 This theorem is referenced by:  a16gbNEW7  29474  a16nfwAUX7  29475  ax16NEW7  29476  hbaew5AUX7  29576  ax7w18AUX7  29604 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-11 1761  ax-12 1950  ax-7v 29369 This theorem depends on definitions:  df-bi 178  df-an 361  df-ex 1551  df-nf 1554
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