Theorem lem3.3.3lem3 1051

Description: Lemma for lem3.3.3 1052. (Contributed by Roy F. Longton, 27-Jun-2005.) (Revised by Roy F. Longton, 3-Jul-2005.)

Assertion

Ref	Expression
lem3.3.3lem3	(a ≡5 b) ≤ ((a →1 b) ∩ (b →1 a))

Proof of Theorem lem3.3.3lem3

Step	Hyp	Ref	Expression
1		lem3.3.3lem1 1049	. 2 (a ≡5 b) ≤ (a →1 b)
2		lem3.3.3lem2 1050	. 2 (a ≡5 b) ≤ (b →1 a)
3	1, 2	ler2an 173	1 (a ≡5 b) ≤ ((a →1 b) ∩ (b →1 a))

Syntax hints:   ≤ wle 2   ∩ wa 7   →₁ wi1 12   ≡₅ wid5 22

This theorem was proved from 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

This theorem depends on definitions:  df-a 40  df-t 41  df-f 42  df-i1 44  df-le1 130  df-le2 131  df-id5 1047

This theorem is referenced by:  lem3.3.3  1052