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Theorem 3eqtr4rd 2080
Description: A deduction from three chained equalities. (Contributed by NM, 21-Sep-1995.)
Hypotheses
Ref Expression
3eqtr4d.1 (φA = B)
3eqtr4d.2 (φ𝐶 = A)
3eqtr4d.3 (φ𝐷 = B)
Assertion
Ref Expression
3eqtr4rd (φ𝐷 = 𝐶)

Proof of Theorem 3eqtr4rd
StepHypRef Expression
1 3eqtr4d.3 . . 3 (φ𝐷 = B)
2 3eqtr4d.1 . . 3 (φA = B)
31, 2eqtr4d 2072 . 2 (φ𝐷 = A)
4 3eqtr4d.2 . 2 (φ𝐶 = A)
53, 4eqtr4d 2072 1 (φ𝐷 = 𝐶)
Colors of variables: wff set class
Syntax hints:  wi 4   = wceq 1242
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1333  ax-gen 1335  ax-4 1397  ax-17 1416  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-cleq 2030
This theorem is referenced by:  csbcnvg  4462  recexnq  6374  prarloclemcalc  6485  addcomprg  6554  mulcomprg  6556  mulcmpblnrlemg  6668  axmulass  6757  divnegap  7465  cjreb  9094  recj  9095  imcj  9103  imval2  9122
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