Theorem gomaex3h5 886

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

Hypotheses

Ref	Expression
gomaex3h5.11	r = ((p_|_ ->1 q)_|_ ^ (c v d))
gomaex3h5.16	k = r
gomaex3h5.17	m = (p_|_ ->1 q)

Assertion

Ref	Expression
gomaex3h5	k =< m_|_

Proof of Theorem gomaex3h5

Step	Hyp	Ref	Expression
1		gomaex3h5.11	. . 3 r = ((p_|_ ->1 q)_|_ ^ (c v d))
2		lea 152	. . 3 ((p_|_ ->1 q)_|_ ^ (c v d)) =< (p_|_ ->1 q)_|_
3	1, 2	bltr 130	. 2 r =< (p_|_ ->1 q)_|_
4		gomaex3h5.16	. 2 k = r
5		gomaex3h5.17	. . 3 m = (p_|_ ->1 q)
6	5	ax-r4 36	. 2 m_|_ = (p_|_ ->1 q)_|_
7	3, 4, 6	le3tr1 132	1 k =< m_|_

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-le1 122  df-le2 123

metamath.org