Theorem ltrelpi 3811

Description: Positive integer 'less than' is a relation on positive integers.

Assertion

Ref	Expression
ltrelpi	⊢ <N ⊆ (N × N)

Proof of Theorem ltrelpi

Step	Hyp	Ref	Expression
1		df-lti 3797	. 2 ⊢ <N = (E ∩ (N × N))
2		inss2 1658	. 2 ⊢ (E ∩ (N × N)) ⊆ (N × N)
3	1, 2	eqsstr 1530	1 ⊢ <N ⊆ (N × N)

Syntax hints:   ∩ cin 1486   ⊆ wss 1487  Ecep 2056   × cxp 2408  Ncnpi 3766   <_N clti 3769

This theorem is referenced by:  ltapi 3824  ltmpi 3825  nlt1pi 3827  indpi 3828  ordpipq 3850  ltsopq 3869

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6  ax-4 673  ax-5 674  ax-6 675  ax-7 676  ax-gen 677  ax-8 798  ax-9 799  ax-10 800  ax-11 801  ax-12 802  ax-16 922  ax-17 925  ax-ext 1074

This theorem depends on definitions:  df-bi 128  df-an 198  df-ex 679  df-sb 853  df-clab 1093  df-cleq 1097  df-clel 1099  df-v 1349  df-in 1491  df-ss 1492  df-lti 3797

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