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Theorem int-eqtransd 40813
Description: EqualityTransitivity generator rule. (Contributed by Stanislas Polu, 7-Apr-2020.)
Hypotheses
Ref Expression
int-eqtransd.1 (𝜑𝐴 = 𝐵)
int-eqtransd.2 (𝜑𝐵 = 𝐶)
Assertion
Ref Expression
int-eqtransd (𝜑𝐴 = 𝐶)

Proof of Theorem int-eqtransd
StepHypRef Expression
1 int-eqtransd.1 . 2 (𝜑𝐴 = 𝐵)
2 int-eqtransd.2 . 2 (𝜑𝐵 = 𝐶)
31, 2eqtrd 2859 1 (𝜑𝐴 = 𝐶)
Colors of variables: wff setvar class
Syntax hints:  wi 4   = wceq 1538
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-9 2125  ax-ext 2796
This theorem depends on definitions:  df-bi 210  df-an 400  df-ex 1782  df-cleq 2817
This theorem is referenced by: (None)
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