|   | Metamath Proof Explorer | < Previous  
      Next > Nearby theorems | |
| Mirrors > Home > MPE Home > Th. List > a1i13 | Structured version Visualization version GIF version | ||
| Description: Add two antecedents to a wff. (Contributed by Jeff Hankins, 4-Aug-2009.) | 
| Ref | Expression | 
|---|---|
| a1i13.1 | ⊢ (𝜓 → 𝜃) | 
| Ref | Expression | 
|---|---|
| a1i13 | ⊢ (𝜑 → (𝜓 → (𝜒 → 𝜃))) | 
| Step | Hyp | Ref | Expression | 
|---|---|---|---|
| 1 | a1i13.1 | . . 3 ⊢ (𝜓 → 𝜃) | |
| 2 | 1 | a1d 25 | . 2 ⊢ (𝜓 → (𝜒 → 𝜃)) | 
| 3 | 2 | a1i 11 | 1 ⊢ (𝜑 → (𝜓 → (𝜒 → 𝜃))) | 
| Colors of variables: wff setvar class | 
| Syntax hints: → wi 4 | 
| This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 | 
| This theorem is referenced by: propeqop 5512 seqshft2 14069 seqsplit 14076 resqrex 15289 2mulprm 16730 comppfsc 23540 filconn 23891 sinq12ge0 26550 usgr2pth 29784 elwspths2on 29980 frgr3vlem1 30292 3vfriswmgrlem 30296 onsupnmax 43240 cantnfresb 43337 dflim5 43342 | 
| Copyright terms: Public domain | W3C validator |