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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
StepHypRef Expression
1 elisset 3120 . . 3
2 nfa1 1897 . . . 4
3 ceqsalg.1 . . . 4
4 ceqsalg.2 . . . . . . 7
54biimpd 207 . . . . . 6
65a2i 13 . . . . 5
76sps 1865 . . . 4
82, 3, 7exlimd 1914 . . 3
91, 8syl5com 30 . 2
104biimprcd 225 . . 3
113, 10alrimi 1877 . 2
129, 11impbid1 203 1
Colors of variables: wff setvar class
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
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