Theorem ltrelpi 5004

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 4990	. 2 |- <N = (E i^i (N. X. N.))
2		inss2 2229	. 2 |- (E i^i (N. X. N.)) (_ (N. X. N.)
3	1, 2	eqsstr 2089	1 |- <N (_ (N. X. N.)

Syntax hints:   i^i cin 2044   (_ wss 2045  Ecep 2827   X. cxp 3165  N.cnpi 4959   <N clti 4962

This theorem is referenced by:  ltapi 5017  ltmpi 5018  nlt1pi 5020  indpi 5021  ordpipq 5043  ltsopq 5062

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 961  ax-gen 962  ax-8 963  ax-10 965  ax-12 967  ax-17 970  ax-4 972  ax-5o 974  ax-6o 977  ax-9o 1122  ax-10o 1139  ax-16 1210  ax-11o 1218  ax-ext 1459

This theorem depends on definitions:  df-bi 147  df-an 225  df-ex 980  df-sb 1172  df-clab 1464  df-cleq 1469  df-clel 1472  df-v 1810  df-in 2049  df-ss 2051  df-lti 4990

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