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Theorem ax13 2155
 Description: Derive ax-13 2104 from ax13v 2105 via axc9 2154. This shows that the weakening in ax13v 2105 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 1957 . . . 4
21con3i 142 . . 3
3 sp 1957 . . . 4
43con3i 142 . . 3
5 axc9 2154 . . 3
62, 4, 5syl2im 38 . 2
7 ax13b 1882 . 2
86, 7mpbir 214 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wi 4  wal 1450 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1677  ax-4 1690  ax-5 1766  ax-6 1813  ax-7 1859  ax-10 1932  ax-12 1950  ax-13 2104 This theorem depends on definitions:  df-bi 190  df-an 378  df-ex 1672  df-nf 1676 This theorem is referenced by:  equvini  2195  sbequi  2224
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