Theorem 19.20d 693

Description: Deduction from Theorem 19.20 of [Margaris] p. 90.

Hypotheses

Ref	Expression
19.20d.1	⊢ (φ → ∀xφ)
19.20d.2	⊢ (φ → (ψ → χ))

Assertion

Ref	Expression
19.20d	⊢ (φ → (∀xψ → ∀xχ))

Proof of Theorem 19.20d

Step	Hyp	Ref	Expression
1		19.20d.1	. 2 ⊢ (φ → ∀xφ)
2		19.20d.2	. . 3 ⊢ (φ → (ψ → χ))
3	2	19.20ii 692	. 2 ⊢ (∀xφ → (∀xψ → ∀xχ))
4	1, 3	syl 12	1 ⊢ (φ → (∀xψ → ∀xχ))

Syntax hints:   → wi 2  ∀wal 672

This theorem is referenced by:  hbald 790  hbsb4 905  19.20dv 946  r19.20da 1255  axacndlem4 3756

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-mp 6  ax-4 673  ax-5 674  ax-gen 677

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