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Theorem bj-sngleq 31077
 Description: Substitution property for sngl. (Contributed by BJ, 6-Oct-2018.)
Assertion
Ref Expression
bj-sngleq sngl sngl

Proof of Theorem bj-sngleq
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 rexeq 3004 . . 3
21abbidv 2538 . 2
3 df-bj-sngl 31076 . 2 sngl
4 df-bj-sngl 31076 . 2 sngl
52, 3, 43eqtr4g 2468 1 sngl sngl
 Colors of variables: wff setvar class Syntax hints:   wi 4   wceq 1405  cab 2387  wrex 2754  csn 3971  sngl bj-csngl 31075 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1639  ax-4 1652  ax-5 1725  ax-6 1771  ax-7 1814  ax-10 1861  ax-11 1866  ax-12 1878  ax-13 2026  ax-ext 2380 This theorem depends on definitions:  df-bi 185  df-an 369  df-tru 1408  df-ex 1634  df-nf 1638  df-sb 1764  df-clab 2388  df-cleq 2394  df-clel 2397  df-nfc 2552  df-rex 2759  df-bj-sngl 31076 This theorem is referenced by:  bj-tageq  31086
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