Theorem ceqsalgALT 3135

Description: Alternate proof of ceqsalg 3134, not using ceqsalt 3132. (Contributed by NM, 29-Oct-2003.) (Proof shortened by Andrew Salmon, 8-Jun-2011.) (Revised by BJ, 29-Sep-2019.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
ceqsalg.1
ceqsalg.2

Assertion

Ref	Expression
ceqsalgALT

Distinct variable group:   ,

Proof of Theorem ceqsalgALT

Step	Hyp	Ref	Expression
1		elisset 3120	. . 3
2		nfa1 1897	. . . 4
3		ceqsalg.1	. . . 4
4		ceqsalg.2	. . . . . . 7
5	4	biimpd 207	. . . . . 6
6	5	a2i 13	. . . . 5
7	6	sps 1865	. . . 4
8	2, 3, 7	exlimd 1914	. . 3
9	1, 8	syl5com 30	. 2
10	4	biimprcd 225	. . 3
11	3, 10	alrimi 1877	. 2
12	9, 11	impbid1 203	1

Syntax hints:  ->wi 4  <->wb 184  A.wal 1393  =wceq 1395  E.wex 1612  F/wnf 1616  e.wcel 1818

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  ax-10 1837  ax-12 1854  ax-ext 2435

This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-v 3111