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

Theorem eqsstrdi 3207
Description: A chained subclass and equality deduction. (Contributed by Mario Carneiro, 2-Jan-2017.)
Hypotheses
Ref Expression
eqsstrdi.1 (𝜑𝐴 = 𝐵)
eqsstrdi.2 𝐵𝐶
Assertion
Ref Expression
eqsstrdi (𝜑𝐴𝐶)

Proof of Theorem eqsstrdi
StepHypRef Expression
1 eqsstrdi.1 . 2 (𝜑𝐴 = 𝐵)
2 eqsstrdi.2 . . 3 𝐵𝐶
32a1i 9 . 2 (𝜑𝐵𝐶)
41, 3eqsstrd 3191 1 (𝜑𝐴𝐶)
Colors of variables: wff set class
Syntax hints:  wi 4   = wceq 1353  wss 3129
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1447  ax-7 1448  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-8 1504  ax-11 1506  ax-4 1510  ax-17 1526  ax-i9 1530  ax-ial 1534  ax-i5r 1535  ax-ext 2159
This theorem depends on definitions:  df-bi 117  df-nf 1461  df-sb 1763  df-clab 2164  df-cleq 2170  df-clel 2173  df-in 3135  df-ss 3142
This theorem is referenced by:  eqsstrrdi  3208  resasplitss  5395  fimacnv  5645  en2other2  7194  exmidfodomrlemim  7199  pw1on  7224  suplocexprlemex  7720  1arith  12364  ennnfonelemkh  12412  aprap  13374  toponsspwpwg  13492  ntrss2  13591  cnprcl2k  13676  reldvg  14118  bj-nntrans  14673  nninfsellemsuc  14731
  Copyright terms: Public domain W3C validator