Theorem 3simpa 1025

Description: Simplification of triple conjunction. (Contributed by NM, 21-Apr-1994.)

Assertion

Ref	Expression
3simpa	|- ( ( ph /\ ps /\ ch ) -> ( ph /\ ps ) )

Proof of Theorem 3simpa

Step	Hyp	Ref	Expression
1		df-3an 1011	. 2 |- ( ( ph /\ ps /\ ch ) <-> ( ( ph /\ ps ) /\ ch ) )
2	1	simplbi 274	1 |- ( ( ph /\ ps /\ ch ) -> ( ph /\ ps ) )

This proof depends on syntax axioms:   -> wi 4   /\ wa 104   /\ w3a 1009

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106

This proof depends on definitions:  df-bi 117  df-3an 1011

This theorem is used by:  3simpb  1026  3simpc  1027  simp1  1028  simp2  1029  3adant3  1048  3adantl3  1186  3adantr3  1189  opprc  3925  oprcl  3928  opm  4374  funtpg  5432  ftpg  5899  ovig  6210  prltlu  7854  mullocpr  7938  lt2halves  9545  nn0n0n1ge2  9719  ixxssixx  10314  pfxsuffeqwrdeq  11484  pfxccatpfx1  11522  pfxccatpfx2  11523  sumtp  12197  dvdsmulcr  12604  dvds2add  12608  dvds2sub  12609  dvdstr  12611  dfgrp3me  13954  uhgrissubgr  16600  subgrprop3  16601  0uhgrsubgr  16604  wlkex  16664  wlkelwrd  16692  bj-peano4  17079