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Theorem dfdisj2 3738
Description: Alternate definition for disjoint classes. (Contributed by NM, 17-Jun-2017.)
Assertion
Ref Expression
dfdisj2 (Disj x A By∃*x(x A y B))
Distinct variable groups:   x,y   y,A   y,B
Allowed substitution hints:   A(x)   B(x)

Proof of Theorem dfdisj2
StepHypRef Expression
1 df-disj 3737 . 2 (Disj x A By∃*x A y B)
2 df-rmo 2308 . . 3 (∃*x A y B∃*x(x A y B))
32albii 1356 . 2 (y∃*x A y By∃*x(x A y B))
41, 3bitri 173 1 (Disj x A By∃*x(x A y B))
Colors of variables: wff set class
Syntax hints:   wa 97  wb 98  wal 1240   wcel 1390  ∃*wmo 1898  ∃*wrmo 2303  Disj wdisj 3736
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1333  ax-gen 1335
This theorem depends on definitions:  df-bi 110  df-rmo 2308  df-disj 3737
This theorem is referenced by:  disjss1  3742  nfdisjv  3748  invdisj  3750  sndisj  3751  disjxsn  3753
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