Theorem ontr1 4929

Description: Transitive law for ordinal numbers. Theorem 7M(b) of [Enderton] p. 192. (Contributed by NM, 11-Aug-1994.)

Assertion

Ref	Expression
ontr1

Proof of Theorem ontr1

Step	Hyp	Ref	Expression
1		eloni 4893	. 2
2		ordtr1 4926	. 2
3	1, 2	syl 16	1

Syntax hints:  ->wi 4  /\wa 369  e.wcel 1818  Ordword 4882  con0 4883

This theorem is referenced by:  smoiun  7051  dif20el  7174  oeordi  7255  omabs  7315  omsmolem  7321  cofsmo  8670  cfsmolem  8671  inar1  9174  grur1a  9218

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  ax-ext 2435

This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ral 2812  df-rex 2813  df-v 3111  df-in 3482  df-ss 3489  df-uni 4250  df-tr 4546  df-po 4805  df-so 4806  df-fr 4843  df-we 4845  df-ord 4886  df-on 4887