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Theorem ax13 2047
 Description: Derive ax-13 1999 from ax13v 2000 via axc9 2046. This shows that the weakening in ax13v 2000 is still sufficient for a complete system. (Contributed by NM, 21-Dec-2015.) (Proof shortened by Wolf Lammen, 31-Jan-2018.)
Assertion
Ref Expression
ax13

Proof of Theorem ax13
StepHypRef Expression
1 sp 1859 . . . 4
21con3i 135 . . 3
3 sp 1859 . . . 4
43con3i 135 . . 3
5 axc9 2046 . . 3
62, 4, 5syl2im 38 . 2
7 ax13b 1805 . 2
86, 7mpbir 209 1
 Colors of variables: wff setvar class Syntax hints:  -.wn 3  ->wi 4  A.wal 1393 This theorem is referenced by:  equvini  2087  sbequi  2116 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-12 1854  ax-13 1999 This theorem depends on definitions:  df-bi 185  df-an 371  df-ex 1613  df-nf 1617
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