Theorem hypstkdOLD 705

Description: Obsolete proof of mpidan 704 as of 28-Mar-2021. (Contributed by Stanislas Polu, 9-Mar-2020.) (New usage is discouraged.) (Proof modification is discouraged.)

Hypotheses

Ref	Expression
mpidan.1	⊢ (𝜑 → 𝜒)
mpidan.2	⊢ (((𝜑 ∧ 𝜓) ∧ 𝜒) → 𝜃)

Assertion

Ref	Expression
hypstkdOLD	⊢ ((𝜑 ∧ 𝜓) → 𝜃)

Proof of Theorem hypstkdOLD

Step	Hyp	Ref	Expression
1		id 22	. 2 ⊢ ((𝜑 ∧ 𝜓) → (𝜑 ∧ 𝜓))
2		mpidan.1	. . 3 ⊢ (𝜑 → 𝜒)
3	2	adantr 481	. 2 ⊢ ((𝜑 ∧ 𝜓) → 𝜒)
4		mpidan.2	. 2 ⊢ (((𝜑 ∧ 𝜓) ∧ 𝜒) → 𝜃)
5	1, 3, 4	syl2anc 693	1 ⊢ ((𝜑 ∧ 𝜓) → 𝜃)

Syntax hints:   → wi 4   ∧ wa 384

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 197  df-an 386

This theorem is referenced by: (None)