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Theorem 3exbidv 1629
 Description: Formula-building rule for 3 existential quantifiers (deduction rule). (Contributed by NM, 1-May-1995.)
Hypothesis
Ref Expression
3exbidv.1 (φ → (ψχ))
Assertion
Ref Expression
3exbidv (φ → (xyzψxyzχ))
Distinct variable groups:   φ,x   φ,y   φ,z
Allowed substitution hints:   ψ(x,y,z)   χ(x,y,z)

Proof of Theorem 3exbidv
StepHypRef Expression
1 3exbidv.1 . . 3 (φ → (ψχ))
21exbidv 1626 . 2 (φ → (zψzχ))
322exbidv 1628 1 (φ → (xyzψxyzχ))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ↔ wb 176  ∃wex 1541 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616 This theorem depends on definitions:  df-bi 177  df-ex 1542 This theorem is referenced by:  ceqsex6v  2899  ins2keq  4218  ins3keq  4219  opkelins2kg  4251  opkelins3kg  4252  oprabid  5550  eloprabga  5578
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