Theorem abcdtb 41093

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	|- ( ( ( ph /\ ps ) /\ ch ) /\ th )

Assertion

Ref	Expression
abcdtb	|- ps

Proof of Theorem abcdtb

Step	Hyp	Ref	Expression
1		abcdtb.1	. . . 4 |- ( ( ( ph /\ ps ) /\ ch ) /\ th )
2	1	simpli 474	. . 3 |- ( ( ph /\ ps ) /\ ch )
3	2	simpli 474	. 2 |- ( ph /\ ps )
4	3	simpri 478	1 |- ps

Syntax hints:   /\ 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)