Theorem gomaex3h8 889

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

Hypotheses

Ref	Expression
gomaex3h8.19	u = (p_|_ ^ q)
gomaex3h8.20	w = q_|_

Assertion

Ref	Expression
gomaex3h8	u =< w_|_

Proof of Theorem gomaex3h8

Step	Hyp	Ref	Expression
1		lear 153	. . 3 (p_|_ ^ q) =< q
2		ax-a1 29	. . 3 q = q_|__|_
3	1, 2	lbtr 131	. 2 (p_|_ ^ q) =< q_|__|_
4		gomaex3h8.19	. 2 u = (p_|_ ^ q)
5		gomaex3h8.20	. . 3 w = q_|_
6	5	ax-r4 36	. 2 w_|_ = q_|__|_
7	3, 4, 6	le3tr1 132	1 u =< w_|_

Syntax hints:   = wb 1   =< wle 2  _|_wn 4   ^ wa 7

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-le1 122  df-le2 123

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