Theorem ltrelpi 10810

Description: Positive integer 'less than' is a relation on positive integers. (Contributed by NM, 8-Feb-1996.) (New usage is discouraged.)

Assertion

Ref	Expression
ltrelpi	⊢ <N ⊆ (N × N)

Proof of Theorem ltrelpi

Step	Hyp	Ref	Expression
1		df-lti 10796	. 2 ⊢ <N = ( E ∩ (N × N))
2		inss2 4173	. 2 ⊢ ( E ∩ (N × N)) ⊆ (N × N)
3	1, 2	eqsstri 3968	1 ⊢ <N ⊆ (N × N)

Syntax hints:   ∩ cin 3889   ⊆ wss 3890   E cep 5524   × cxp 5623  Ncnpi 10765   <_N clti 10768

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1802  ax-4 1816  ax-5 1917  ax-6 1974  ax-7 2015  ax-8 2121  ax-9 2129  ax-ext 2712

This theorem depends on definitions:  df-bi 208  df-an 397  df-tru 1550  df-ex 1787  df-sb 2074  df-clab 2719  df-cleq 2732  df-clel 2815  df-rab 3393  df-v 3434  df-in 3897  df-ss 3907  df-lti 10796

This theorem is referenced by:  ltapi  10824  ltmpi  10825  nlt1pi  10827  indpi  10828  ordpipq  10863  ltsonq  10890  archnq  10901