Theorem 19.35i 755

Description: Inference from Theorem 19.35 of [Margaris] p. 90.

Hypothesis

Ref	Expression
19.35i.1	⊢ ∃x(φ → ψ)

Assertion

Ref	Expression
19.35i	⊢ (∀xφ → ∃xψ)

Proof of Theorem 19.35i

Step	Hyp	Ref	Expression
1		19.35i.1	. 2 ⊢ ∃x(φ → ψ)
2		19.35 754	. 2 ⊢ (∃x(φ → ψ) ↔ (∀xφ → ∃xψ))
3	1, 2	mpbi 164	1 ⊢ (∀xφ → ∃xψ)

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

This theorem is referenced by:  zfrep2 1475  zfcndext 3759  zfcndrep 3760  zfcndinf 3764

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

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

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