Theorem 19.36v 958

Description: Special case of Theorem 19.36 of [Margaris] p. 90.

Assertion

Ref	Expression
19.36v	⊢ (∃x(φ → ψ) ↔ (∀xφ → ψ))

Distinct variable group(s):   ψ,x

Proof of Theorem 19.36v

Step	Hyp	Ref	Expression
1		ax-17 925	. 2 ⊢ (ψ → ∀xψ)
2	1	19.36 757	1 ⊢ (∃x(φ → ψ) ↔ (∀xφ → ψ))

Syntax hints:   → wi 2   ↔ wb 127  ∀wal 672  ∃wex 678

This theorem is referenced by:  19.12vv 960  axext 1086  vtocl2 1379  vtocl3 1380

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-6 675  ax-gen 677  ax-17 925

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

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