Theorem wleoa 358

Description: Relation between two methods of expressing "less than or equal to".

Hypothesis

Ref	Expression
wleoa.1	((a ∪ c) ≡ b) = 1

Assertion

Ref	Expression
wleoa	((a ∩ b) ≡ a) = 1

Proof of Theorem wleoa

Step	Hyp	Ref	Expression
1		wleoa.1	. . . 4 ((a ∪ c) ≡ b) = 1
2	1	wr1 189	. . 3 (b ≡ (a ∪ c)) = 1
3	2	wlan 352	. 2 ((a ∩ b) ≡ (a ∩ (a ∪ c))) = 1
4		wa5c 193	. 2 ((a ∩ (a ∪ c)) ≡ a) = 1
5	3, 4	wr2 353	1 ((a ∩ b) ≡ a) = 1

Syntax hints:   = wb 1   ≡ tb 5   ∪ wo 6   ∩ wa 7  1wt 9

This theorem is referenced by:  wdf2le2 368

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-wom 343

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

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