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Theorem ax13b 1805
Description: Two equivalent ways of expressing ax-13 1999. See the comment for ax-13 1999. (Contributed by NM, 2-May-2017.) (Proof shortened by Wolf Lammen, 26-Feb-2018.)
Assertion
Ref Expression
ax13b

Proof of Theorem ax13b
StepHypRef Expression
1 ax-1 6 . . 3
2 equtrr 1797 . . . . . . 7
32equcoms 1795 . . . . . 6
43con3rr3 136 . . . . 5
54imim1d 75 . . . 4
6 pm2.43 51 . . . 4
75, 6syl6 33 . . 3
81, 7impbid2 204 . 2
98pm5.74i 245 1
Colors of variables: wff setvar class
Syntax hints:  -.wn 3  ->wi 4  <->wb 184  A.wal 1393
This theorem is referenced by:  ax13  2047
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
This theorem depends on definitions:  df-bi 185  df-ex 1613
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