Theorem ltrelpi 11001

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 10987	. 2 ⊢ <N = ( E ∩ (N × N))
2		inss2 4137	. 2 ⊢ ( E ∩ (N × N)) ⊆ (N × N)
3	1, 2	eqsstri 3959	1 ⊢ <N ⊆ (N × N)

This proof depends on syntax axioms:   ⊆ wss 3900   ∩ cin 4092   E cep 5554   × cxp 5653  Ncnpi 10956   <_N clti 10959

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1828  ax-4 1842  ax-5 1945  ax-6 2002  ax-7 2043  ax-8 2149  ax-9 2157  ax-ext 2735

This proof depends on definitions:  df-bi 210  df-an 402  df-tru 1573  df-ex 1813  df-sb 2102  df-clab 2742  df-cleq 2755  df-clel 2839  df-rab 3417  df-v 3456  df-ss 3901  df-in 4094  df-lti 10987

This theorem is used by:  ltapi  11015  ltmpi  11016  nlt1pi  11018  indpi  11019  ordpipq  11054  ltsonq  11081  archnq  11092