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Theorem 2rexbidva 2341
 Description: Formula-building rule for restricted existential quantifiers (deduction rule). (Contributed by NM, 15-Dec-2004.)
Hypothesis
Ref Expression
2ralbidva.1 ((φ (x A y B)) → (ψχ))
Assertion
Ref Expression
2rexbidva (φ → (x A y B ψx A y B χ))
Distinct variable groups:   x,y,φ   y,A
Allowed substitution hints:   ψ(x,y)   χ(x,y)   A(x)   B(x,y)

Proof of Theorem 2rexbidva
StepHypRef Expression
1 2ralbidva.1 . . . 4 ((φ (x A y B)) → (ψχ))
21anassrs 380 . . 3 (((φ x A) y B) → (ψχ))
32rexbidva 2317 . 2 ((φ x A) → (y B ψy B χ))
43rexbidva 2317 1 (φ → (x A y B ψx A y B χ))
 Colors of variables: wff set class Syntax hints:   → wi 4   ∧ wa 97   ↔ wb 98   ∈ wcel 1390  ∃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: (None)
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