Theorem int-eqtransd 41806

Description: EqualityTransitivity generator rule. (Contributed by Stanislas Polu, 7-Apr-2020.)

Hypotheses

Ref	Expression
int-eqtransd.1	⊢ (𝜑 → 𝐴 = 𝐵)
int-eqtransd.2	⊢ (𝜑 → 𝐵 = 𝐶)

Assertion

Ref	Expression
int-eqtransd	⊢ (𝜑 → 𝐴 = 𝐶)

Proof of Theorem int-eqtransd

Step	Hyp	Ref	Expression
1		int-eqtransd.1	. 2 ⊢ (𝜑 → 𝐴 = 𝐵)
2		int-eqtransd.2	. 2 ⊢ (𝜑 → 𝐵 = 𝐶)
3	1, 2	eqtrd 2779	1 ⊢ (𝜑 → 𝐴 = 𝐶)

Syntax hints:   → wi 4   = wceq 1539

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1914  ax-6 1972  ax-7 2012  ax-9 2117  ax-ext 2710

This theorem depends on definitions:  df-bi 206  df-an 397  df-ex 1783  df-cleq 2731

This theorem is referenced by: (None)