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Theorem equs5e 1979
Description: A property related to substitution that unlike equs5 2092 doesn't require a distinctor antecedent. (Contributed by NM, 2-Feb-2007.) (Proof shortened by Wolf Lammen, 15-Jan-2018.)
Assertion
Ref Expression
equs5e

Proof of Theorem equs5e
StepHypRef Expression
1 nfa1 1897 . 2
2 hbe1 1839 . . . . 5
3219.23bi 1871 . . . 4
4 ax-12 1854 . . . 4
53, 4syl5 32 . . 3
65imp 429 . 2
71, 6exlimi 1912 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  /\wa 369  A.wal 1393  E.wex 1612
This theorem is referenced by:  sb4e  1998
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
This theorem depends on definitions:  df-bi 185  df-an 371  df-ex 1613  df-nf 1617
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