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Theorem sbequ8 1744
Description: Elimination of equality from antecedent after substitution. (Contributed by NM, 5-Aug-1993.) Reduce dependencies on axioms. (Revised by Wolf Lammen, 28-Jul-2018.)
Assertion
Ref Expression
sbequ8

Proof of Theorem sbequ8
StepHypRef Expression
1 pm5.4 362 . . . 4
21bicomi 202 . . 3
3 abai 795 . . . 4
43exbii 1667 . . 3
52, 4anbi12i 697 . 2
6 df-sb 1740 . 2
7 df-sb 1740 . 2
85, 6, 73bitr4i 277 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  <->wb 184  /\wa 369  E.wex 1612  [wsb 1739
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631
This theorem depends on definitions:  df-bi 185  df-an 371  df-ex 1613  df-sb 1740
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