Theorem u5lem1 720

Description: Lemma for unified implication study.

Assertion

Ref	Expression
u5lem1	((a →5 b) →5 a) = ((a ∪ b) ∩ (a ∪ b⊥ ))

Proof of Theorem u5lem1

Step	Hyp	Ref	Expression
1		u5lemc1 666	. . . 4 a C (a →5 b)
2	1	comcom 435	. . 3 (a →5 b) C a
3	2	u5lemc4 687	. 2 ((a →5 b) →5 a) = ((a →5 b)⊥ ∪ a)
4		u5lemnoa 646	. 2 ((a →5 b)⊥ ∪ a) = ((a ∪ b) ∩ (a ∪ b⊥ ))
5	3, 4	ax-r2 35	1 ((a →5 b) →5 a) = ((a ∪ b) ∩ (a ∪ b⊥ ))

Syntax hints:   = wb 1  ^⊥ wn 4   ∪ wo 6   ∩ wa 7   →₅ wi5 17

This theorem is referenced by:  u5lem1n 725

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-i5 47  df-le1 122  df-le2 123  df-c1 124  df-c2 125

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