Theorem abcdtb 44308

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

Hypothesis

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

Assertion

Ref	Expression
abcdtb	⊢ 𝜓

Proof of Theorem abcdtb

Step	Hyp	Ref	Expression
1		abcdtb.1	. . . 4 ⊢ (((𝜑 ∧ 𝜓) ∧ 𝜒) ∧ 𝜃)
2	1	simpli 483	. . 3 ⊢ ((𝜑 ∧ 𝜓) ∧ 𝜒)
3	2	simpli 483	. 2 ⊢ (𝜑 ∧ 𝜓)
4	3	simpri 485	1 ⊢ 𝜓

Syntax hints:   ∧ wa 395

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 396

This theorem is referenced by: (None)