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Theorem 3exbii 1495
Description: Inference adding 3 existential quantifiers to both sides of an equivalence. (Contributed by NM, 2-May-1995.)
Hypothesis
Ref Expression
exbii.1 (φψ)
Assertion
Ref Expression
3exbii (xyzφxyzψ)

Proof of Theorem 3exbii
StepHypRef Expression
1 exbii.1 . . 3 (φψ)
21exbii 1493 . 2 (zφzψ)
322exbii 1494 1 (xyzφxyzψ)
Colors of variables: wff set class
Syntax hints:  wb 98  wex 1378
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  ax-ie1 1379  ax-ie2 1380  ax-4 1397  ax-ial 1424
This theorem depends on definitions:  df-bi 110
This theorem is referenced by:  eeeanv  1805  ceqsex6v  2592  oprabid  5480  dfoprab2  5494  dftpos3  5818  xpassen  6240
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