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Theorem 2exbidv 1745
Description: Formula-building rule for 2 existential quantifiers (deduction rule). (Contributed by NM, 1-May-1995.)
Hypothesis
Ref Expression
2albidv.1 (φ → (ψχ))
Assertion
Ref Expression
2exbidv (φ → (xyψxyχ))
Distinct variable groups:   φ,x   φ,y
Allowed substitution hints:   ψ(x,y)   χ(x,y)

Proof of Theorem 2exbidv
StepHypRef Expression
1 2albidv.1 . . 3 (φ → (ψχ))
21exbidv 1703 . 2 (φ → (yψyχ))
32exbidv 1703 1 (φ → (xyψxyχ))
Colors of variables: wff set class
Syntax hints:  wi 4  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-17 1416  ax-ial 1424
This theorem depends on definitions:  df-bi 110
This theorem is referenced by:  3exbidv  1746  4exbidv  1747  cbvex4v  1802  ceqsex3v  2590  ceqsex4v  2591  copsexg  3972  euotd  3982  elopab  3986  elxpi  4304  relop  4429  cbvoprab3  5522  ov6g  5580  th3qlem1  6144  ltresr  6696
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