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Theorem ax12 2019
 Description: Derive ax-12 1950 from ax12v 1951 via ax12o 2010. This shows that the weakening in ax12v 1951 is still sufficient for a complete system. (Contributed by NM, 21-Dec-2015.) (Proof shortened by Wolf Lammen, 31-Jan-2018.)
Assertion
Ref Expression
ax12

Proof of Theorem ax12
StepHypRef Expression
1 sp 1763 . . . 4
21con3i 129 . . 3
3 sp 1763 . . . 4
43con3i 129 . . 3
5 ax12o 2010 . . 3
62, 4, 5syl2im 36 . 2
7 ax12b 1701 . 2
86, 7mpbir 201 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4  wal 1549 This theorem is referenced by:  dveeq1  2021 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-7 1749  ax-11 1761  ax-12 1950 This theorem depends on definitions:  df-bi 178  df-an 361  df-ex 1551  df-nf 1554
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