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Theorem eqeq12 2049
 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 2043 . 2 (A = B → (A = 𝐶B = 𝐶))
2 eqeq2 2046 . 2 (𝐶 = 𝐷 → (B = 𝐶B = 𝐷))
31, 2sylan9bb 435 1 ((A = B 𝐶 = 𝐷) → (A = 𝐶B = 𝐷))
 Colors of variables: wff set class Syntax hints:   → wi 4   ∧ wa 97   ↔ wb 98   = wceq 1242 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-gen 1335  ax-4 1397  ax-17 1416  ax-ext 2019 This theorem depends on definitions:  df-bi 110  df-cleq 2030 This theorem is referenced by:  eqeq12i  2050  eqeq12d  2051  eqeqan12d  2052  funopg  4877  tfri3  5894  th3qlem1  6144  xpdom2  6241  xrlttri3  8448
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