Theorem 19.36aiv 959

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

Hypothesis

Ref	Expression
19.36aiv.1	⊢ ∃x(φ → ψ)

Assertion

Ref	Expression
19.36aiv	⊢ (∀xφ → ψ)

Distinct variable group(s):   ψ,x

Proof of Theorem 19.36aiv

Step	Hyp	Ref	Expression
1		ax-17 925	. 2 ⊢ (ψ → ∀xψ)
2		19.36aiv.1	. 2 ⊢ ∃x(φ → ψ)
3	1, 2	19.36i 758	1 ⊢ (∀xφ → ψ)

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

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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