Theorem 19.36i 758

Description: Inference from Theorem 19.36 of [Margaris] p. 90.

Hypotheses

Ref	Expression
19.36i.1	⊢ (ψ → ∀xψ)
19.36i.2	⊢ ∃x(φ → ψ)

Assertion

Ref	Expression
19.36i	⊢ (∀xφ → ψ)

Proof of Theorem 19.36i

Step	Hyp	Ref	Expression
1		19.36i.2	. 2 ⊢ ∃x(φ → ψ)
2		19.36i.1	. . 3 ⊢ (ψ → ∀xψ)
3	2	19.36 757	. 2 ⊢ (∃x(φ → ψ) ↔ (∀xφ → ψ))
4	1, 3	mpbi 164	1 ⊢ (∀xφ → ψ)

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

This theorem is referenced by:  19.36aiv 959  vtoclf 1377

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

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

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