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Theorem eqeq12 2034
Description: Equality relationship among 4 classes. (Contributed by NM, 3-Aug-1994.)
Assertion
Ref Expression
eqeq12 ((A = B 𝐶 = 𝐷) → (A = 𝐶B = 𝐷))

Proof of Theorem eqeq12
StepHypRef Expression
1 eqeq1 2028 . 2 (A = B → (A = 𝐶B = 𝐶))
2 eqeq2 2031 . 2 (𝐶 = 𝐷 → (B = 𝐶B = 𝐷))
31, 2sylan9bb 438 1 ((A = B 𝐶 = 𝐷) → (A = 𝐶B = 𝐷))
Colors of variables: wff set class
Syntax hints:  wi 4   wa 97  wb 98   = wceq 1228
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 1316  ax-gen 1318  ax-4 1381  ax-17 1400  ax-ext 2004
This theorem depends on definitions:  df-bi 110  df-cleq 2015
This theorem is referenced by:  eqeq12i  2035  eqeq12d  2036  eqeqan12d  2037  funopg  4860  tfri3  5875  th3qlem1  6119
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