Theorem int-eqtransd 38491

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

Hypotheses

Ref	Expression
int-eqtransd.1	|- ( ph -> A = B )
int-eqtransd.2	|- ( ph -> B = C )

Assertion

Ref	Expression
int-eqtransd	|- ( ph -> A = C )

Proof of Theorem int-eqtransd

Step	Hyp	Ref	Expression
1		int-eqtransd.1	. 2 |- ( ph -> A = B )
2		int-eqtransd.2	. 2 |- ( ph -> B = C )
3	1, 2	eqtrd 2656	1 |- ( ph -> A = C )

Syntax hints:   -> wi 4   = wceq 1483

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-9 1999  ax-ext 2602

This theorem depends on definitions:  df-bi 197  df-an 386  df-ex 1705  df-cleq 2615

This theorem is referenced by: (None)