Theorem 3anassrs 1231

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 1227	. 2 |- ( ph -> ( ps -> ( ch -> ( th -> ta ) ) ) )
3	2	imp41 353	1 |- ( ( ( ( ph /\ ps ) /\ ch ) /\ th ) -> ta )

Syntax hints:   -> wi 4   /\ wa 104   /\ w3a 980

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

This theorem depends on definitions:  df-bi 117  df-3an 982

This theorem is referenced by:  ralrimivvva  2580  euotd  4287  dfgrp3me  13232  kerf1ghm  13404  neitx  14504  xmetpsmet  14605