Theorem gomaex3h4 885

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

Hypotheses

Ref	Expression
gomaex3h4.11	r = ((p_|_ ->1 q)_|_ ^ (c v d))
gomaex3h4.15	j = (c v d)_|_
gomaex3h4.16	k = r

Assertion

Ref	Expression
gomaex3h4	j =< k_|_

Proof of Theorem gomaex3h4

Step	Hyp	Ref	Expression
1		gomaex3h4.11	. . . 4 r = ((p_|_ ->1 q)_|_ ^ (c v d))
2		lear 153	. . . 4 ((p_|_ ->1 q)_|_ ^ (c v d)) =< (c v d)
3	1, 2	bltr 130	. . 3 r =< (c v d)
4	3	lecon 146	. 2 (c v d)_|_ =< r_|_
5		gomaex3h4.15	. 2 j = (c v d)_|_
6		gomaex3h4.16	. . 3 k = r
7	6	ax-r4 36	. 2 k_|_ = r_|_
8	4, 5, 7	le3tr1 132	1 j =< k_|_

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

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