Theorem ad5ant235OLD 1476

Description: Obsolete version of ad5ant235 1475 as of 14-Apr-2022. (Contributed by Alan Sare, 17-Oct-2017.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypothesis

Ref	Expression
ad5ant.1	⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜃)

Assertion

Ref	Expression
ad5ant235OLD	⊢ (((((𝜏 ∧ 𝜑) ∧ 𝜓) ∧ 𝜂) ∧ 𝜒) → 𝜃)

Proof of Theorem ad5ant235OLD

Step	Hyp	Ref	Expression
1		ad5ant.1	. . . . . . . 8 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜃)
2	1	3exp 1149	. . . . . . 7 ⊢ (𝜑 → (𝜓 → (𝜒 → 𝜃)))
3	2	a1ddd 80	. . . . . 6 ⊢ (𝜑 → (𝜓 → (𝜒 → (𝜏 → 𝜃))))
4	3	a1ddd 80	. . . . 5 ⊢ (𝜑 → (𝜓 → (𝜒 → (𝜂 → (𝜏 → 𝜃)))))
5	4	com5r 104	. . . 4 ⊢ (𝜏 → (𝜑 → (𝜓 → (𝜒 → (𝜂 → 𝜃)))))
6	5	com45 97	. . 3 ⊢ (𝜏 → (𝜑 → (𝜓 → (𝜂 → (𝜒 → 𝜃)))))
7	6	imp 396	. 2 ⊢ ((𝜏 ∧ 𝜑) → (𝜓 → (𝜂 → (𝜒 → 𝜃))))
8	7	imp41 417	1 ⊢ (((((𝜏 ∧ 𝜑) ∧ 𝜓) ∧ 𝜂) ∧ 𝜒) → 𝜃)

Syntax hints:   → wi 4   ∧ wa 385   ∧ w3a 1108

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 199  df-an 386  df-3an 1110

This theorem is referenced by: (None)