Theorem gomaex3h7 888

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

Hypotheses

Ref	Expression
gomaex3h7.18	n = (p_|_ ->1 q)_|_
gomaex3h7.19	u = (p_|_ ^ q)

Assertion

Ref	Expression
gomaex3h7	n =< u_|_

Proof of Theorem gomaex3h7

Step	Hyp	Ref	Expression
1		leor 151	. . . 4 (p_|_ ^ q) =< (p_|__|_ v (p_|_ ^ q))
2		df-i1 43	. . . . 5 (p_|_ ->1 q) = (p_|__|_ v (p_|_ ^ q))
3	2	ax-r1 34	. . . 4 (p_|__|_ v (p_|_ ^ q)) = (p_|_ ->1 q)
4	1, 3	lbtr 131	. . 3 (p_|_ ^ q) =< (p_|_ ->1 q)
5	4	lecon 146	. 2 (p_|_ ->1 q)_|_ =< (p_|_ ^ q)_|_
6		gomaex3h7.18	. 2 n = (p_|_ ->1 q)_|_
7		gomaex3h7.19	. . 3 u = (p_|_ ^ q)
8	7	ax-r4 36	. 2 u_|_ = (p_|_ ^ q)_|_
9	5, 6, 8	le3tr1 132	1 n =< u_|_

Syntax hints:   = wb 1   =< wle 2  _|_wn 4   v wo 6   ^ wa 7   ->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-i1 43  df-le1 122  df-le2 123

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