Theorem mlaconj2 828

Description: For 5GO proof of Mladen's conjecture. Hypothesis is 5GO law consequence.

Hypothesis

Ref	Expression
mlaconj2.1	((((a ->1 (a ^ b)) ^ ((a ^ b) ->1 ((a ^ b) v c))) ^ ((((a ^ b) v c) ->1 c) ^ (c ->1 (a v b)))) ^ ((a v b) ->1 a)) =< (a == c)

Assertion

Ref	Expression
mlaconj2	((a == b) ^ ((a == c) v (b == c))) =< (a == c)

Proof of Theorem mlaconj2

Step	Hyp	Ref	Expression
1		mlaconj 827	. 2 ((a == b) ^ ((a == c) v (b == c))) =< ((((a ->1 (a ^ b)) ^ ((a ^ b) ->1 ((a ^ b) v c))) ^ ((((a ^ b) v c) ->1 c) ^ (c ->1 (a v b)))) ^ ((a v b) ->1 a))
2		mlaconj2.1	. 2 ((((a ->1 (a ^ b)) ^ ((a ^ b) ->1 ((a ^ b) v c))) ^ ((((a ^ b) v c) ->1 c) ^ (c ->1 (a v b)))) ^ ((a v b) ->1 a)) =< (a == c)
3	1, 2	letr 129	1 ((a == b) ^ ((a == c) v (b == c))) =< (a == c)

Syntax hints:   =< wle 2   == tb 5   v wo 6   ^ wa 7   ->1 wi1 13

This theorem was proved from axioms:  ax-a1 29  ax-a2 30  ax-a3 31  ax-a4 32  ax-a5 33  ax-r1 34  ax-r2 35  ax-r4 36  ax-r5 37  ax-r3 421

This theorem depends on definitions:  df-b 38  df-a 39  df-t 40  df-f 41  df-i1 43  df-i2 44  df-le1 122  df-le2 123  df-c1 124  df-c2 125

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