Theorem 3simpa 996

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

Assertion

Ref	Expression
3simpa	⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → (𝜑 ∧ 𝜓))

Proof of Theorem 3simpa

Step	Hyp	Ref	Expression
1		df-3an 982	. 2 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) ↔ ((𝜑 ∧ 𝜓) ∧ 𝜒))
2	1	simplbi 274	1 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → (𝜑 ∧ 𝜓))

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

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

This theorem is referenced by:  3simpb  997  3simpc  998  simp1  999  simp2  1000  3adant3  1019  3adantl3  1157  3adantr3  1160  opprc  3830  oprcl  3833  opm  4268  funtpg  5310  ftpg  5747  ovig  6045  prltlu  7556  mullocpr  7640  lt2halves  9229  nn0n0n1ge2  9398  ixxssixx  9979  sumtp  11581  dvdsmulcr  11988  dvds2add  11992  dvds2sub  11993  dvdstr  11995  dfgrp3me  13242  bj-peano4  15611