Theorem int-eqtransd 45188

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 2795	1 ⊢ (𝜑 → 𝐴 = 𝐶)

This proof depends on syntax axioms:   → wi 4   = wceq 1569

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1827  ax-4 1841  ax-5 1942  ax-6 1999  ax-7 2040  ax-9 2154  ax-ext 2732

This proof depends on definitions:  df-bi 210  df-an 402  df-ex 1812  df-cleq 2752

This theorem is used by: (None)