Theorem nfbidOLD 1833

Description: Obsolete proof of nfbid 1832 as of 29-Dec-2017. (Contributed by Mario Carneiro, 24-Sep-2016.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
nfbid.1	⊢ (φ → Ⅎxψ)
nfbid.2	⊢ (φ → Ⅎxχ)

Assertion

Ref	Expression
nfbidOLD	⊢ (φ → Ⅎx(ψ ↔ χ))

Proof of Theorem nfbidOLD

Step	Hyp	Ref	Expression
1		dfbi1 184	. 2 ⊢ ((ψ ↔ χ) ↔ ¬ ((ψ → χ) → ¬ (χ → ψ)))
2		nfbid.1	. . . . 5 ⊢ (φ → Ⅎxψ)
3		nfbid.2	. . . . 5 ⊢ (φ → Ⅎxχ)
4	2, 3	nfimd 1808	. . . 4 ⊢ (φ → Ⅎx(ψ → χ))
5	3, 2	nfimd 1808	. . . . 5 ⊢ (φ → Ⅎx(χ → ψ))
6	5	nfnd 1791	. . . 4 ⊢ (φ → Ⅎx ¬ (χ → ψ))
7	4, 6	nfimd 1808	. . 3 ⊢ (φ → Ⅎx((ψ → χ) → ¬ (χ → ψ)))
8	7	nfnd 1791	. 2 ⊢ (φ → Ⅎx ¬ ((ψ → χ) → ¬ (χ → ψ)))
9	1, 8	nfxfrd 1571	1 ⊢ (φ → Ⅎx(ψ ↔ χ))

This proof depends on syntax axioms:  ¬ wn 3   → wi 4   ↔ wb 176  Ⅎwnf 1544

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-11 1746

This proof depends on definitions:  df-bi 177  df-ex 1542  df-nf 1545

This theorem is used by: (None)