Theorem hbimdOLD 2230

Description: Obsolete proof of hbimd 2126 as of 6-Oct-2021. (Contributed by NM, 14-May-1993.) (Proof shortened by Wolf Lammen, 3-Jan-2018.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
hbimdOLD.1	⊢ (𝜑 → ∀𝑥𝜑)
hbimdOLD.2	⊢ (𝜑 → (𝜓 → ∀𝑥𝜓))
hbimdOLD.3	⊢ (𝜑 → (𝜒 → ∀𝑥𝜒))

Assertion

Ref	Expression
hbimdOLD	⊢ (𝜑 → ((𝜓 → 𝜒) → ∀𝑥(𝜓 → 𝜒)))

Proof of Theorem hbimdOLD

Step	Hyp	Ref	Expression
1		hbimdOLD.1	. . . 4 ⊢ (𝜑 → ∀𝑥𝜑)
2		hbimdOLD.2	. . . 4 ⊢ (𝜑 → (𝜓 → ∀𝑥𝜓))
3	1, 2	nfdhOLD 2194	. . 3 ⊢ (𝜑 → Ⅎ𝑥𝜓)
4		hbimdOLD.3	. . . 4 ⊢ (𝜑 → (𝜒 → ∀𝑥𝜒))
5	1, 4	nfdhOLD 2194	. . 3 ⊢ (𝜑 → Ⅎ𝑥𝜒)
6	3, 5	nfimdOLD 2226	. 2 ⊢ (𝜑 → Ⅎ𝑥(𝜓 → 𝜒))
7	6	nfrdOLD 2190	1 ⊢ (𝜑 → ((𝜓 → 𝜒) → ∀𝑥(𝜓 → 𝜒)))

Syntax hints:   → wi 4  ∀wal 1481

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-10 2019  ax-12 2047

This theorem depends on definitions:  df-bi 197  df-or 385  df-ex 1705  df-nf 1710  df-nfOLD 1721

This theorem is referenced by: (None)