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Theorem ax13b 1859
 Description: An equivalence used to show two ways of expressing ax-13 2057. See the comment for ax-13 2057. (Contributed by NM, 2-May-2017.) (Proof shortened by Wolf Lammen, 26-Feb-2018.) (Revised by BJ, 15-Sep-2020.)
Assertion
Ref Expression
ax13b

Proof of Theorem ax13b
StepHypRef Expression
1 ax-1 6 . . 3
2 equtrr 1851 . . . . . . 7
32equcoms 1849 . . . . . 6
43con3rr3 141 . . . . 5
54imim1d 78 . . . 4
6 pm2.43 53 . . . 4
75, 6syl6 34 . . 3
81, 7impbid2 207 . 2
98pm5.74i 248 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wi 4   wb 187 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1663  ax-4 1676  ax-5 1752  ax-6 1798  ax-7 1843 This theorem depends on definitions:  df-bi 188  df-ex 1658 This theorem is referenced by:  ax13  2106
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