Theorem imim21b 367

Description: Simplify an implication between two implications when the antecedent of the first is a consequence of the antecedent of the second. The reverse form is useful in producing the successor step in induction proofs. (Contributed by Paul Chapman, 22-Jun-2011.) (Proof shortened by Wolf Lammen, 14-Sep-2013.)

Assertion

Ref	Expression
imim21b

Proof of Theorem imim21b

Step	Hyp	Ref	Expression
1		bi2.04 361	. 2
2		pm5.5 336	. . . . 5
3	2	imbi1d 317	. . . 4
4	3	imim2i 14	. . 3
5	4	pm5.74d 247	. 2
6	1, 5	syl5bb 257	1

Syntax hints:  ->wi 4  <->wb 184

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 185