Theorem pm3.2an3 1240

Description: Version of pm3.2 463 for a triple conjunction. (Contributed by Alan Sare, 24-Oct-2011.) (Proof shortened by Kyle Wyonch, 24-Apr-2021.)

Assertion

Ref	Expression
pm3.2an3	|- ( ph -> ( ps -> ( ch -> ( ph /\ ps /\ ch ) ) ) )

Proof of Theorem pm3.2an3

Step	Hyp	Ref	Expression
1		df-3an 1039	. . 3 |- ( ( ph /\ ps /\ ch ) <-> ( ( ph /\ ps ) /\ ch ) )
2	1	biimpri 218	. 2 |- ( ( ( ph /\ ps ) /\ ch ) -> ( ph /\ ps /\ ch ) )
3	2	exp31 630	1 |- ( ph -> ( ps -> ( ch -> ( ph /\ ps /\ ch ) ) ) )

Syntax hints:   -> wi 4   /\ wa 384   /\ w3a 1037

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  df-3an 1039

This theorem is referenced by:  3exp  1264  tratrb  38746  19.21a3con13vVD  39087  tratrbVD  39097