Theorem 19.37v 961

Description: Special case of Theorem 19.37 of [Margaris] p. 90.

Assertion

Ref	Expression
19.37v	⊢ (∃x(φ → ψ) ↔ (φ → ∃xψ))

Distinct variable group(s):   φ,x

Proof of Theorem 19.37v

Step	Hyp	Ref	Expression
1		ax-17 925	. 2 ⊢ (φ → ∀xφ)
2	1	19.37 759	1 ⊢ (∃x(φ → ψ) ↔ (φ → ∃xψ))

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

This theorem is referenced by:  19.37aiv 962  moanim 1051  zfrep3 1476  ssiun 2018  iununi 2037  bnd 3548  kmlem14 3593  kmlem15 3594

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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