Theorem ordtr1 3007

Description: Transitive law for ordinal classes.

Assertion

Ref	Expression
ordtr1	|- (Ord C -> ((A e. B /\ B e. C) -> A e. C))

Proof of Theorem ordtr1

Step	Hyp	Ref	Expression
1		ordtr 2968	. 2 |- (Ord C -> Tr C)
2		trel 2692	. 2 |- (Tr C -> ((A e. B /\ B e. C) -> A e. C))
3	1, 2	syl 10	1 |- (Ord C -> ((A e. B /\ B e. C) -> A e. C))

Syntax hints:   -> wi 3   /\ wa 223   e. wcel 960  Tr wtr 2685  Ord word 2953

This theorem is referenced by:  ordtr2 3008  ontr1 3009  oarec 4202

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 964  ax-gen 965  ax-8 966  ax-10 968  ax-12 970  ax-17 973  ax-4 975  ax-5o 977  ax-6o 980  ax-9o 1125  ax-10o 1142  ax-16 1212  ax-11o 1220  ax-ext 1462

This theorem depends on definitions:  df-bi 147  df-an 225  df-ex 983  df-sb 1174  df-clab 1467  df-cleq 1472  df-clel 1475  df-v 1815  df-in 2054  df-ss 2056  df-uni 2508  df-tr 2686  df-ord 2957

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