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Theorem eqeq12 2052
Description: Equality relationship among 4 classes. (Contributed by NM, 3-Aug-1994.)
Assertion
Ref Expression
eqeq12 ((𝐴 = 𝐵𝐶 = 𝐷) → (𝐴 = 𝐶𝐵 = 𝐷))

Proof of Theorem eqeq12
StepHypRef Expression
1 eqeq1 2046 . 2 (𝐴 = 𝐵 → (𝐴 = 𝐶𝐵 = 𝐶))
2 eqeq2 2049 . 2 (𝐶 = 𝐷 → (𝐵 = 𝐶𝐵 = 𝐷))
31, 2sylan9bb 435 1 ((𝐴 = 𝐵𝐶 = 𝐷) → (𝐴 = 𝐶𝐵 = 𝐷))
Colors of variables: wff set class
Syntax hints:  wi 4  wa 97  wb 98   = wceq 1243
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 1336  ax-gen 1338  ax-4 1400  ax-17 1419  ax-ext 2022
This theorem depends on definitions:  df-bi 110  df-cleq 2033
This theorem is referenced by:  eqeq12i  2053  eqeq12d  2054  eqeqan12d  2055  funopg  4934  tfri3  5953  th3qlem1  6208  xpdom2  6305  xrlttri3  8718
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