Theorem 3anassrs 1219

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 1215	. 2 |- ( ph -> ( ps -> ( ch -> ( th -> ta ) ) ) )
3	2	imp41 351	1 |- ( ( ( ( ph /\ ps ) /\ ch ) /\ th ) -> ta )

Syntax hints:   -> wi 4   /\ wa 103   /\ w3a 968

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107

This theorem depends on definitions:  df-bi 116  df-3an 970

This theorem is referenced by:  ralrimivvva  2549  euotd  4232  neitx  12908  xmetpsmet  13009