Theorem a2and 811

Description: Deduction distributing a conjunction as embedded antecedent. (Contributed by AV, 25-Oct-2019.) (Proof shortened by Wolf Lammen, 19-Jan-2020.)

Hypotheses

Ref	Expression
a2and.1
a2and.2

Assertion

Ref	Expression
a2and

Proof of Theorem a2and

Step	Hyp	Ref	Expression
1		a2and.2	. . . . . . 7
2	1	expd 436	. . . . . 6
3	2	imdistand 692	. . . . 5
4	3	imp 429	. . . 4
5		a2and.1	. . . . 5
6	5	imp 429	. . . 4
7	4, 6	embantd 54	. . 3
8	7	ex 434	. 2
9	8	com23 78	1

Syntax hints:  ->wi 4  /\wa 369

This theorem is referenced by:  telgsumfzs  17018

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  df-an 371