Theorem 3anassrs 1173

Description: Associative law for conjunction applied to antecedent (eliminates syllogism). (Contributed by Mario Carneiro, 4-Jan-2017.)

Hypothesis

Ref	Expression
3anassrs.1	|- ((ph /\ (ps /\ ch /\ th)) -> ta)

Assertion

Ref	Expression
3anassrs	|- ((((ph /\ ps) /\ ch) /\ th) -> ta)

Proof of Theorem 3anassrs

Step	Hyp	Ref	Expression
1		3anassrs.1	. . 3 |- ((ph /\ (ps /\ ch /\ th)) -> ta)
2	1	3exp2 1169	. 2 |- (ph -> (ps -> (ch -> (th -> ta))))
3	2	imp41 576	1 |- ((((ph /\ ps) /\ ch) /\ th) -> ta)

Syntax hints:   -> wi 4   /\ wa 358   /\ w3a 934

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 177  df-an 360  df-3an 936

This theorem is referenced by: (None)