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Mirrors > Home > ILE Home > Th. List > simp3d | GIF version |
Description: Deduce a conjunct from a triple conjunction. (Contributed by NM, 4-Sep-2005.) |
Ref | Expression |
---|---|
3simp1d.1 | ⊢ (𝜑 → (𝜓 ∧ 𝜒 ∧ 𝜃)) |
Ref | Expression |
---|---|
simp3d | ⊢ (𝜑 → 𝜃) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 3simp1d.1 | . 2 ⊢ (𝜑 → (𝜓 ∧ 𝜒 ∧ 𝜃)) | |
2 | simp3 906 | . 2 ⊢ ((𝜓 ∧ 𝜒 ∧ 𝜃) → 𝜃) | |
3 | 1, 2 | syl 14 | 1 ⊢ (𝜑 → 𝜃) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∧ w3a 885 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 |
This theorem depends on definitions: df-bi 110 df-3an 887 |
This theorem is referenced by: simp3bi 921 erinxp 6180 addcanprleml 6712 addcanprlemu 6713 ltmprr 6740 lelttrdi 7421 ixxdisj 8772 ixxss1 8773 ixxss2 8774 ixxss12 8775 iccsupr 8835 icodisj 8860 intfracq 9162 flqdiv 9163 cjmul 9485 |
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