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Theorem int-eqprincd 40812
Description: PrincipleOfEquality generator rule. (Contributed by Stanislas Polu, 7-Apr-2020.)
Hypotheses
Ref Expression
int-eqprincd.1 (𝜑𝐴 = 𝐵)
int-eqprincd.2 (𝜑𝐶 = 𝐷)
Assertion
Ref Expression
int-eqprincd (𝜑 → (𝐴 + 𝐶) = (𝐵 + 𝐷))

Proof of Theorem int-eqprincd
StepHypRef Expression
1 int-eqprincd.1 . 2 (𝜑𝐴 = 𝐵)
2 int-eqprincd.2 . 2 (𝜑𝐶 = 𝐷)
31, 2oveq12d 7167 1 (𝜑 → (𝐴 + 𝐶) = (𝐵 + 𝐷))
Colors of variables: wff setvar class
Syntax hints:  wi 4   = wceq 1538  (class class class)co 7149   + caddc 10538
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1912  ax-6 1971  ax-7 2016  ax-8 2117  ax-9 2125  ax-ext 2796
This theorem depends on definitions:  df-bi 210  df-an 400  df-or 845  df-3an 1086  df-ex 1782  df-sb 2071  df-clab 2803  df-cleq 2817  df-clel 2896  df-v 3482  df-un 3924  df-in 3926  df-ss 3936  df-sn 4551  df-pr 4553  df-op 4557  df-uni 4825  df-br 5053  df-iota 6302  df-fv 6351  df-ov 7152
This theorem is referenced by: (None)
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