Theorem nom34 315

Description: Part of Lemma 3.3(14) from "Non-Orthomodular Models..." paper.

Assertion

Ref	Expression
nom34	((a ∩ b) ≡4 a) = (a →1 b)

Proof of Theorem nom34

Step	Hyp	Ref	Expression
1		nomb41 291	. 2 ((a ∩ b) ≡4 a) = (a ≡1 (a ∩ b))
2		nom21 306	. 2 (a ≡1 (a ∩ b)) = (a →1 b)
3	1, 2	ax-r2 35	1 ((a ∩ b) ≡4 a) = (a →1 b)

Syntax hints:   = wb 1   ∩ wa 7   →₁ wi1 13   ≡₁ wid1 19   ≡₄ wid4 22

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

This theorem depends on definitions:  df-a 39  df-t 40  df-f 41  df-i1 43  df-id1 49  df-id4 52  df-le1 122  df-le2 123

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