Theorem sonr 2850

Description: A strict order relation is irreflexive.

Assertion

Ref	Expression
sonr	|- ((R Or A /\ B e. A) -> -. BRB)

Proof of Theorem sonr

Step	Hyp	Ref	Expression
1		poirr 2840	. 2 |- ((R Po A /\ B e. A) -> -. BRB)
2		sopo 2846	. 2 |- (R Or A -> R Po A)
3	1, 2	sylan 448	1 |- ((R Or A /\ B e. A) -> -. BRB)

Syntax hints:  -. wn 2   -> wi 3   /\ wa 223   e. wcel 956   class class class wbr 2614   Po wpo 2833   Or wor 2834

This theorem is referenced by:  sotric 2855  sotrieq 2856  soirri 3434  suppr 4570  supsnALT 4572  1ne0sr 5185  ltnrt 5511

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 960  ax-gen 961  ax-8 962  ax-10 964  ax-12 966  ax-17 969  ax-4 971  ax-5o 973  ax-6o 976  ax-9o 1121  ax-10o 1138  ax-16 1208  ax-11o 1216  ax-ext 1457

This theorem depends on definitions:  df-bi 147  df-or 224  df-an 225  df-3an 776  df-ex 979  df-sb 1170  df-clab 1462  df-cleq 1467  df-clel 1470  df-ral 1646  df-v 1808  df-un 2046  df-sn 2408  df-pr 2409  df-op 2412  df-br 2615  df-po 2835  df-so 2845

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