Theorem ltrelpi 10468

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 10454	. 2 ⊢ <N = ( E ∩ (N × N))
2		inss2 4130	. 2 ⊢ ( E ∩ (N × N)) ⊆ (N × N)
3	1, 2	eqsstri 3921	1 ⊢ <N ⊆ (N × N)

Syntax hints:   ∩ cin 3852   ⊆ wss 3853   E cep 5444   × cxp 5534  Ncnpi 10423   <_N clti 10426

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1803  ax-4 1817  ax-5 1918  ax-6 1976  ax-7 2018  ax-8 2114  ax-9 2122  ax-ext 2708

This theorem depends on definitions:  df-bi 210  df-an 400  df-tru 1546  df-ex 1788  df-sb 2073  df-clab 2715  df-cleq 2728  df-clel 2809  df-rab 3060  df-v 3400  df-in 3860  df-ss 3870  df-lti 10454

This theorem is referenced by:  ltapi  10482  ltmpi  10483  nlt1pi  10485  indpi  10486  ordpipq  10521  ltsonq  10548  archnq  10559