Theorem 3adantr1 1170

Description: Deduction adding a conjunct to antecedent. (Contributed by NM, 27-Apr-2005.)

Hypothesis

Ref	Expression
3adantr.1	⊢ ((𝜑 ∧ (𝜓 ∧ 𝜒)) → 𝜃)

Assertion

Ref	Expression
3adantr1	⊢ ((𝜑 ∧ (𝜏 ∧ 𝜓 ∧ 𝜒)) → 𝜃)

Proof of Theorem 3adantr1

Step	Hyp	Ref	Expression
1		3simpc 1150	. 2 ⊢ ((𝜏 ∧ 𝜓 ∧ 𝜒) → (𝜓 ∧ 𝜒))
2		3adantr.1	. 2 ⊢ ((𝜑 ∧ (𝜓 ∧ 𝜒)) → 𝜃)
3	1, 2	sylan2 593	1 ⊢ ((𝜑 ∧ (𝜏 ∧ 𝜓 ∧ 𝜒)) → 𝜃)

Syntax hints:   → wi 4   ∧ wa 395   ∧ w3a 1086

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 207  df-an 396  df-3an 1088

This theorem is referenced by:  3adant3r1  1183  3ad2antr3  1191  swopo  5550  omeulem1  8523  divmuldiv  11858  imasmnd2  18677  imasgrp2  18963  imasrng  20062  srgbinomlem2  20112  imasring  20215  abvdiv  20714  mdetunilem9  22483  lly1stc  23359  icccvx  24824  dchrpt  27154  dipsubdir  30750  poimirlem4  37591  fdc  37712  unichnidl  37998  dmncan1  38043  pexmidlem6N  39942  erngdvlem3  40957  erngdvlem3-rN  40965  dvalveclem  40992  dvhvaddass  41064  dvhlveclem  41075  issmflem  46698  prproropf1olem3  47479