Theorem hb3anOLD 1831

Description: Obsolete proof of hb3an 1830 as of 2-Jan-2018. (Contributed by NM, 14-Sep-2003.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

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

Assertion

Ref	Expression
hb3anOLD	⊢ ((φ ∧ ψ ∧ χ) → ∀x(φ ∧ ψ ∧ χ))

Proof of Theorem hb3anOLD

Step	Hyp	Ref	Expression
1		df-3an 936	. 2 ⊢ ((φ ∧ ψ ∧ χ) ↔ ((φ ∧ ψ) ∧ χ))
2		hb.1	. . . 4 ⊢ (φ → ∀xφ)
3		hb.2	. . . 4 ⊢ (ψ → ∀xψ)
4	2, 3	hban 1828	. . 3 ⊢ ((φ ∧ ψ) → ∀x(φ ∧ ψ))
5		hb.3	. . 3 ⊢ (χ → ∀xχ)
6	4, 5	hban 1828	. 2 ⊢ (((φ ∧ ψ) ∧ χ) → ∀x((φ ∧ ψ) ∧ χ))
7	1, 6	hbxfrbi 1568	1 ⊢ ((φ ∧ ψ ∧ χ) → ∀x(φ ∧ ψ ∧ χ))

This proof depends on syntax axioms:   → wi 4   ∧ wa 358   ∧ w3a 934  ∀wal 1540

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-an 360  df-3an 936  df-tru 1319  df-ex 1542  df-nf 1545

This theorem is used by: (None)