ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  sseq12 Structured version   GIF version

Theorem sseq12 2962
Description: Equality theorem for the subclass relationship. (Contributed by NM, 31-May-1999.)
Assertion
Ref Expression
sseq12 ((A = B 𝐶 = 𝐷) → (A𝐶B𝐷))

Proof of Theorem sseq12
StepHypRef Expression
1 sseq1 2960 . 2 (A = B → (A𝐶B𝐶))
2 sseq2 2961 . 2 (𝐶 = 𝐷 → (B𝐶B𝐷))
31, 2sylan9bb 435 1 ((A = B 𝐶 = 𝐷) → (A𝐶B𝐷))
Colors of variables: wff set class
Syntax hints:  wi 4   wa 97  wb 98   = wceq 1242  wss 2911
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-11 1394  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-in 2918  df-ss 2925
This theorem is referenced by:  sseq12i  2965  funcnvuni  4911  fun11iun  5090
  Copyright terms: Public domain W3C validator