Theorem abcdtc 39743

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

Hypothesis

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

Assertion

Ref	Expression
abcdtc	⊢ 𝜒

Proof of Theorem abcdtc

Step	Hyp	Ref	Expression
1		abcdtc.1	. . 3 ⊢ (((𝜑 ∧ 𝜓) ∧ 𝜒) ∧ 𝜃)
2	1	simpli 473	. 2 ⊢ ((𝜑 ∧ 𝜓) ∧ 𝜒)
3	2	simpri 477	1 ⊢ 𝜒

Syntax hints:   ∧ 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)