Theorem ltrelpi 5017

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

Assertion

Ref	Expression
ltrelpi	|- <N (_ (N. X. N.)

Proof of Theorem ltrelpi

Step	Hyp	Ref	Expression
1		df-lti 5003	. 2 |- <N = (E i^i (N. X. N.))
2		inss2 2231	. 2 |- (E i^i (N. X. N.)) (_ (N. X. N.)
3	1, 2	eqsstr 2091	1 |- <N (_ (N. X. N.)

Syntax hints:   i^i cin 2046   (_ wss 2047  Ecep 2830   X. cxp 3168  N.cnpi 4972   <N clti 4975

This theorem is referenced by:  ltapi 5030  ltmpi 5031  nlt1pi 5033  indpi 5034  ordpipq 5056  ltsopq 5075

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 962  ax-gen 963  ax-8 964  ax-10 966  ax-12 968  ax-17 971  ax-4 973  ax-5o 975  ax-6o 978  ax-9o 1123  ax-10o 1140  ax-16 1210  ax-11o 1218  ax-ext 1459

This theorem depends on definitions:  df-bi 147  df-an 225  df-ex 981  df-sb 1172  df-clab 1464  df-cleq 1469  df-clel 1472  df-v 1812  df-in 2051  df-ss 2053  df-lti 5003

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