Theorem abcdta 44420

Description: Given (((a and b) and c) and d), there exists a proof for a. (Contributed by Jarvin Udandy, 3-Sep-2016.)

Hypothesis

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

Assertion

Ref	Expression
abcdta	⊢ 𝜑

Proof of Theorem abcdta

Step	Hyp	Ref	Expression
1		abcdta.1	. . . 4 ⊢ (((𝜑 ∧ 𝜓) ∧ 𝜒) ∧ 𝜃)
2	1	simpli 484	. . 3 ⊢ ((𝜑 ∧ 𝜓) ∧ 𝜒)
3	2	simpli 484	. 2 ⊢ (𝜑 ∧ 𝜓)
4	3	simpli 484	1 ⊢ 𝜑

Syntax hints:   ∧ wa 396

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 206  df-an 397

This theorem is referenced by: (None)