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Theorem 2rexbidv 2327
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 2305 . 2 (φ → (y B ψy B χ))
32rexbidv 2305 1 (φ → (x A y B ψx A y B χ))
Colors of variables: wff set class
Syntax hints:  wi 4  wb 98  wrex 2285
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 1316  ax-gen 1318  ax-ie1 1363  ax-ie2 1364  ax-4 1381  ax-17 1400  ax-ial 1409
This theorem depends on definitions:  df-bi 110  df-nf 1330  df-rex 2290
This theorem is referenced by:  f1oiso  5390  elrnmpt2g  5536  elrnmpt2  5537  ralrnmpt2  5538  rexrnmpt2  5539  ovelrn  5572  eroveu  6108  genipv  6363  genpelxp  6365  genpelvl  6366  genpelvu  6367  genpelpw  6371  axcnre  6575
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