Theorem anandis 677

Description: Inference that undistributes conjunction in the antecedent. (Contributed by NM, 7-Jun-2004.)

Hypothesis

Ref	Expression
anandis.1	⊢ (((𝜑 ∧ 𝜓) ∧ (𝜑 ∧ 𝜒)) → 𝜏)

Assertion

Ref	Expression
anandis	⊢ ((𝜑 ∧ (𝜓 ∧ 𝜒)) → 𝜏)

Proof of Theorem anandis

Step	Hyp	Ref	Expression
1		anandis.1	. . 3 ⊢ (((𝜑 ∧ 𝜓) ∧ (𝜑 ∧ 𝜒)) → 𝜏)
2	1	an4s 659	. 2 ⊢ (((𝜑 ∧ 𝜑) ∧ (𝜓 ∧ 𝜒)) → 𝜏)
3	2	anabsan 664	1 ⊢ ((𝜑 ∧ (𝜓 ∧ 𝜒)) → 𝜏)

Syntax hints:   → wi 4   ∧ wa 395

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 206  df-an 396

This theorem is referenced by:  3impdi  1348  dff13  7259  f1oiso  7353  omord2  8581  fodomacn  10071  ltapi  10918  ltmpi  10919  axpre-ltadd  11182  faclbnd  14273  pwsdiagmhm  18774  tgcl  22859  brbtwn2  28703  grpoinvf  30329  ocorth  31088  fh1  31415  fh2  31416  spansncvi  31449  lnopmi  31797  adjlnop  31883  matunitlindflem2  37025  poimirlem4  37032  heicant  37063  mblfinlem2  37066  ismblfin  37069  ftc1anclem6  37106  ftc1anclem7  37107  ftc1anc  37109