Theorem rmoan 3298

Description: Restricted "at most one" still holds when a conjunct is added. (Contributed by NM, 16-Jun-2017.)

Assertion

Ref	Expression
rmoan

Proof of Theorem rmoan

Step	Hyp	Ref	Expression
1		moan 2345	. . 3
2		an12 797	. . . 4
3	2	mobii 2307	. . 3
4	1, 3	sylib 196	. 2
5		df-rmo 2815	. 2
6		df-rmo 2815	. 2
7	4, 5, 6	3imtr4i 266	1

Syntax hints:  ->wi 4  /\wa 369  e.wcel 1818  E*wmo 2283  E*wrmo 2810

This theorem is referenced by:  reuxfr2d  4675  reuxfr3d  27388

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-12 1854

This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-eu 2286  df-mo 2287  df-rmo 2815