Theorem gomaex3h6 887

Description: Hypothesis for Godowski 6-var -> Mayet Example 3.

Hypotheses

Ref	Expression
gomaex3h6.17	m = (p_|_ ->1 q)
gomaex3h6.18	n = (p_|_ ->1 q)_|_

Assertion

Ref	Expression
gomaex3h6	m =< n_|_

Proof of Theorem gomaex3h6

Step	Hyp	Ref	Expression
1		leid 140	. . 3 (p_|_ ->1 q) =< (p_|_ ->1 q)
2		ax-a1 29	. . 3 (p_|_ ->1 q) = (p_|_ ->1 q)_|__|_
3	1, 2	lbtr 131	. 2 (p_|_ ->1 q) =< (p_|_ ->1 q)_|__|_
4		gomaex3h6.17	. 2 m = (p_|_ ->1 q)
5		gomaex3h6.18	. . 3 n = (p_|_ ->1 q)_|_
6	5	ax-r4 36	. 2 n_|_ = (p_|_ ->1 q)_|__|_
7	3, 4, 6	le3tr1 132	1 m =< n_|_

Syntax hints:   = wb 1   =< wle 2  _|_wn 4   ->1 wi1 13

This theorem is referenced by:  gomaex3lem5 898

This theorem was proved from axioms:  ax-a1 29  ax-a2 30  ax-a5 33  ax-r1 34  ax-r2 35  ax-r4 36  ax-r5 37

This theorem depends on definitions:  df-a 39  df-t 40  df-f 41  df-le1 122  df-le2 123

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