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Theorem 2rexbidv 2343
Description: Formula-building rule for restricted existential quantifiers (deduction rule). (Contributed by NM, 28-Jan-2006.)
Hypothesis
Ref Expression
2ralbidv.1 (φ → (ψχ))
Assertion
Ref Expression
2rexbidv (φ → (x A y B ψx A y B χ))
Distinct variable groups:   φ,x   φ,y
Allowed substitution hints:   ψ(x,y)   χ(x,y)   A(x,y)   B(x,y)

Proof of Theorem 2rexbidv
StepHypRef Expression
1 2ralbidv.1 . . 3 (φ → (ψχ))
21rexbidv 2321 . 2 (φ → (y B ψy B χ))
32rexbidv 2321 1 (φ → (x A y B ψx A y B χ))
Colors of variables: wff set class
Syntax hints:  wi 4  wb 98  wrex 2301
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  df-nf 1347  df-rex 2306
This theorem is referenced by:  f1oiso  5408  elrnmpt2g  5555  elrnmpt2  5556  ralrnmpt2  5557  rexrnmpt2  5558  ovelrn  5591  eroveu  6133  genipv  6492  genpelxp  6494  genpelvl  6495  genpelvu  6496  axcnre  6765  apreap  7371  apreim  7387
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