Theorem l42mod 1151

Description: An equation that fails in OML L42 when converted to a Hilbert space equation. (Contributed by NM, 8-Apr-2012.)

Assertion

Ref	Expression
l42mod	((((a ∪ b) ∩ c) ∪ d) ∩ e) ≤ ((a ∪ b) ∪ ((a ∪ d) ∩ (b ∪ e)))

Proof of Theorem l42mod

Step	Hyp	Ref	Expression
1		l42modlem2 1150	. 2 ((((a ∪ b) ∩ c) ∪ d) ∩ e) ≤ (((a ∪ b) ∪ d) ∩ ((a ∪ b) ∪ e))
2		l42modlem1 1149	. 2 (((a ∪ b) ∪ d) ∩ ((a ∪ b) ∪ e)) = ((a ∪ b) ∪ ((a ∪ d) ∩ (b ∪ e)))
3	1, 2	lbtr 139	1 ((((a ∪ b) ∩ c) ∪ d) ∩ e) ≤ ((a ∪ b) ∪ ((a ∪ d) ∩ (b ∪ e)))

This proof depends on syntax axioms:   ≤ wle 2   ∪ wo 6   ∩ wa 7

This proof depends on axioms:  ax-a1 30  ax-a2 31  ax-a3 32  ax-a5 34  ax-r1 35  ax-r2 36  ax-r4 37  ax-r5 38  ax-ml 1122

This proof depends on definitions:  df-a 40  df-t 41  df-f 42  df-le1 130  df-le2 131

This theorem is used by: (None)