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Theorem ax16 1990
 Description: Theorem showing that ax-16 2086 is redundant if ax-17 1604 is included in the axiom system. The important part of the proof is provided by aev 1933. See ax16ALT 2035 for an alternate proof that does not require ax-10 2082 or ax-12o 2084. Axiom ax-16 2086 should not be referenced in any proof. Instead, use this theorem. (Contributed by NM, 8-Nov-2006.)
Assertion
Ref Expression
ax16
Distinct variable group:   ,
Dummy variable is distinct from all other variables.
Allowed substitution hints:   (,)

Proof of Theorem ax16
StepHypRef Expression
1 aev 1933 . 2
2 sbequ12 1861 . . . . 5
32biimpcd 217 . . . 4
43alimdv 1608 . . 3
5 nfv 1606 . . . . 5
65nfs1 1989 . . . 4
7 stdpc7 1859 . . . 4
86, 5, 7cbv3 1924 . . 3
94, 8syl6com 33 . 2
101, 9syl 17 1
 Colors of variables: wff set class Syntax hints:   wi 6  wal 1528  wsb 1631 This theorem is referenced by:  ax11v  2036  hbs1  2044  a16g  2048  exists2  2234 This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-gen 1534  ax-5 1545  ax-17 1604  ax-9 1637  ax-8 1645  ax-6 1704  ax-7 1709  ax-11 1716  ax-12 1867 This theorem depends on definitions:  df-bi 179  df-an 362  df-tru 1312  df-ex 1530  df-nf 1533  df-sb 1632
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