Theorem adant423OLD 819

Description: Obsolete as of 2-Oct-2021. (Contributed by Glauco Siliprandi, 11-Dec-2019.) (New usage is discouraged.) (Proof modification is discouraged.)

Hypothesis

Ref	Expression
adant423.1	⊢ ((𝜑 ∧ 𝜓) → 𝜒)

Assertion

Ref	Expression
adant423OLD	⊢ ((((𝜑 ∧ 𝜃) ∧ 𝜏) ∧ 𝜓) → 𝜒)

Proof of Theorem adant423OLD

Step	Hyp	Ref	Expression
1		simplll 794	. 2 ⊢ ((((𝜑 ∧ 𝜃) ∧ 𝜏) ∧ 𝜓) → 𝜑)
2		adant423.1	. 2 ⊢ ((𝜑 ∧ 𝜓) → 𝜒)
3	1, 2	sylancom 698	1 ⊢ ((((𝜑 ∧ 𝜃) ∧ 𝜏) ∧ 𝜓) → 𝜒)

Syntax hints:   → wi 4   ∧ wa 383

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 196  df-an 385

This theorem is referenced by: (None)