Theorem bi4exdv 940

Description: Formula-building rule for 4 existential quantifiers (deduction rule).

Hypothesis

Ref	Expression
bi4exdv.1	⊢ (φ → (ψ ↔ χ))

Assertion

Ref	Expression
bi4exdv	⊢ (φ → (∃x∃y∃z∃wψ ↔ ∃x∃y∃z∃wχ))

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

Proof of Theorem bi4exdv

Step	Hyp	Ref	Expression
1		bi4exdv.1	. . 3 ⊢ (φ → (ψ ↔ χ))
2	1	bi2exdv 938	. 2 ⊢ (φ → (∃z∃wψ ↔ ∃z∃wχ))
3	2	bi2exdv 938	1 ⊢ (φ → (∃x∃y∃z∃wψ ↔ ∃x∃y∃z∃wχ))

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

This theorem is referenced by:  copsex4g 1904  opbrop 2472  oprabval3 3052  brecop 3242  th3q 3253

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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