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Theorem 2rexbidv 2657
 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 2635 . 2 (φ → (y B ψy B χ))
32rexbidv 2635 1 (φ → (x A y B ψx A y B χ))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ↔ wb 176  ∃wrex 2615 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-11 1746 This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1542  df-nf 1545  df-rex 2620 This theorem is referenced by:  eladdc  4398  f1oiso  5499  ovelrn  5608  mucex  6133
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