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| Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.) (Proof shortened by Wolf Lammen, 23-Jun-2022.) | 
| Ref | Expression | 
|---|---|
| simprl3 | ⊢ ((𝜏 ∧ ((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃)) → 𝜒) | 
| Step | Hyp | Ref | Expression | 
|---|---|---|---|
| 1 | simp3 1139 | . 2 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜒) | |
| 2 | 1 | ad2antrl 728 | 1 ⊢ ((𝜏 ∧ ((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃)) → 𝜒) | 
| Colors of variables: wff setvar class | 
| Syntax hints: → wi 4 ∧ wa 395 ∧ w3a 1087 | 
| 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 1089 | 
| This theorem is referenced by: poxp3 8175 ttrcltr 9756 pwfseqlem5 10703 icodiamlt 15474 issubc3 17894 pgpfac1lem5 20099 clsconn 23438 txlly 23644 txnlly 23645 itg2add 25794 ftc1a 26078 nosupprefixmo 27745 noinfprefixmo 27746 nosupbnd2 27761 noinfbnd2 27776 mulsprop 28156 f1otrg 28879 ax5seglem6 28949 axcontlem10 28988 numclwwlk5 30407 locfinref 33840 btwnouttr2 36023 btwnconn1lem13 36100 midofsegid 36105 outsideofeq 36131 ivthALT 36336 mpaaeu 43162 dfsalgen2 46356 grtrimap 47915 | 
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