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Theorem 2exbidv 1726
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 1684 . 2 (φ → (yψyχ))
32exbidv 1684 1 (φ → (xyψxyχ))
Colors of variables: wff set class
Syntax hints:  wi 4  wb 98  wex 1358
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 1312  ax-gen 1314  ax-ie1 1359  ax-ie2 1360  ax-4 1377  ax-17 1396  ax-ial 1405
This theorem depends on definitions:  df-bi 110
This theorem is referenced by:  3exbidv  1727  4exbidv  1728  cbvex4v  1783  ceqsex3v  2569  ceqsex4v  2570  copsexg  3951  euotd  3961  elopab  3965  elxpi  4284  relop  4409  cbvoprab3  5499  ov6g  5557  th3qlem1  6115  ltresr  6549
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