Theorem gomaex3h3 884

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

Hypotheses

Ref	Expression
gomaex3h3.14	i = c
gomaex3h3.15	j = (c v d)_|_

Assertion

Ref	Expression
gomaex3h3	i =< j_|_

Proof of Theorem gomaex3h3

Step	Hyp	Ref	Expression
1		leo 150	. . 3 c =< (c v d)
2		ax-a1 29	. . 3 (c v d) = (c v d)_|__|_
3	1, 2	lbtr 131	. 2 c =< (c v d)_|__|_
4		gomaex3h3.14	. 2 i = c
5		gomaex3h3.15	. . 3 j = (c v d)_|_
6	5	ax-r4 36	. 2 j_|_ = (c v d)_|__|_
7	3, 4, 6	le3tr1 132	1 i =< j_|_

Syntax hints:   = wb 1   =< wle 2  _|_wn 4   v wo 6

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