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Theorem ceqsalgALT 3049
 Description: Alternate proof of ceqsalg 3048, not using ceqsalt 3046. (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:   ,
Allowed substitution hints:   ()   ()   ()

Proof of Theorem ceqsalgALT
StepHypRef Expression
1 elisset 3033 . . 3
2 nfa1 1956 . . . 4
3 ceqsalg.1 . . . 4
4 ceqsalg.2 . . . . . . 7
54biimpd 210 . . . . . 6
65a2i 14 . . . . 5
76sps 1920 . . . 4
82, 3, 7exlimd 1974 . . 3
91, 8syl5com 31 . 2
104biimprcd 228 . . 3
113, 10alrimi 1932 . 2
129, 11impbid1 206 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 187  wal 1435   wceq 1437  wex 1657  wnf 1661   wcel 1872 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1663  ax-4 1676  ax-5 1752  ax-6 1798  ax-7 1843  ax-10 1891  ax-12 1909  ax-ext 2408 This theorem depends on definitions:  df-bi 188  df-an 372  df-tru 1440  df-ex 1658  df-nf 1662  df-sb 1791  df-clab 2415  df-cleq 2421  df-clel 2424  df-v 3024 This theorem is referenced by: (None)
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