Theorem bi3exdv 939

Description: Formula-building rule for 3 existential quantifiers (deduction rule).

Hypothesis

Ref	Expression
bi3exdv.1	⊢ (φ → (ψ ↔ χ))

Assertion

Ref	Expression
bi3exdv	⊢ (φ → (∃x∃y∃zψ ↔ ∃x∃y∃zχ))

Distinct variable group(s):   φ,x   φ,y   φ,z

Proof of Theorem bi3exdv

Step	Hyp	Ref	Expression
1		bi3exdv.1	. . 3 ⊢ (φ → (ψ ↔ χ))
2	1	biexdv 936	. 2 ⊢ (φ → (∃zψ ↔ ∃zχ))
3	2	bi2exdv 938	1 ⊢ (φ → (∃x∃y∃zψ ↔ ∃x∃y∃zχ))

Syntax hints:   → wi 2   ↔ wb 127  ∃wex 678

This theorem is referenced by:  eloprabg 3035

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6  ax-4 673  ax-5 674  ax-gen 677  ax-17 925

This theorem depends on definitions:  df-bi 128  df-an 198  df-ex 679

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