Theorem sb8mo 2320

Description: Variable substitution for "at most one." (Contributed by Alexander van der Vekens, 17-Jun-2017.)

Hypothesis

Ref	Expression
sb8eu.1

Assertion

Ref	Expression
sb8mo

Proof of Theorem sb8mo

Step	Hyp	Ref	Expression
1		sb8eu.1	. . . 4
2	1	sb8e 2168	. . 3
3	1	sb8eu 2318	. . 3
4	2, 3	imbi12i 326	. 2
5		df-mo 2287	. 2
6		df-mo 2287	. 2
7	4, 5, 6	3bitr4i 277	1

Syntax hints:  ->wi 4  <->wb 184  E.wex 1612  F/wnf 1616  [wsb 1739  E!weu 2282  E*wmo 2283

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-11 1842  ax-12 1854  ax-13 1999

This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-eu 2286  df-mo 2287