Theorem ltrelpi 10803

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 10789	. 2 ⊢ <N = ( E ∩ (N × N))
2		inss2 4179	. 2 ⊢ ( E ∩ (N × N)) ⊆ (N × N)
3	1, 2	eqsstri 3969	1 ⊢ <N ⊆ (N × N)

Syntax hints:   ∩ cin 3889   ⊆ wss 3890   E cep 5523   × cxp 5622  Ncnpi 10758   <_N clti 10761

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1912  ax-6 1969  ax-7 2010  ax-8 2116  ax-9 2124  ax-ext 2709

This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1545  df-ex 1782  df-sb 2069  df-clab 2716  df-cleq 2729  df-clel 2812  df-rab 3391  df-v 3432  df-in 3897  df-ss 3907  df-lti 10789

This theorem is referenced by:  ltapi  10817  ltmpi  10818  nlt1pi  10820  indpi  10821  ordpipq  10856  ltsonq  10883  archnq  10894