Theorem alcomiw 1811

Description: Weak version of alcom 1845. Uses only Tarski's FOL axiom schemes. (Contributed by NM, 10-Apr-2017.)

Hypothesis

Ref	Expression
alcomiw.1

Assertion

Ref	Expression
alcomiw

Distinct variable groups:   ,   ,   ,   ,

Proof of Theorem alcomiw

Step	Hyp	Ref	Expression
1		alcomiw.1	. . . . 5
2	1	biimpd 207	. . . 4
3	2	cbvalivw 1789	. . 3
4	3	alimi 1633	. 2
5		ax-5 1704	. 2
6	1	biimprd 223	. . . . . 6
7	6	equcoms 1795	. . . . 5
8	7	spimvw 1784	. . . 4
9	8	alimi 1633	. . 3
10	9	alimi 1633	. 2
11	4, 5, 10	3syl 20	1

Syntax hints:  ->wi 4  <->wb 184  A.wal 1393

This theorem is referenced by:  hbalw  1816  ax11w  1826

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790

This theorem depends on definitions:  df-bi 185  df-ex 1613