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Theorem equvin 1804
Description: A variable introduction law for equality. Lemma 15 of [Monk2] p. 109. (Contributed by NM, 9-Jan-1993.) Remove dependencies on ax-10 1837, ax-13 1999. (Revised by Wolf Lammen, 10-Jun-2019.)
Assertion
Ref Expression
equvin
Distinct variable groups:   ,   ,

Proof of Theorem equvin
StepHypRef Expression
1 equviniv 1803 . . 3
2 equcom 1794 . . . . 5
32anbi2i 694 . . . 4
43exbii 1667 . . 3
51, 4sylib 196 . 2
6 equtr 1796 . . . 4
76imp 429 . . 3
87exlimiv 1722 . 2
95, 8impbii 188 1
Colors of variables: wff setvar class
Syntax hints:  <->wb 184  /\wa 369  E.wex 1612
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
This theorem depends on definitions:  df-bi 185  df-an 371  df-ex 1613
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