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Theorem syl6reqr 2404
 Description: An equality transitivity deduction. (Contributed by NM, 29-Mar-1998.)
Hypotheses
Ref Expression
syl6reqr.1 (φA = B)
syl6reqr.2 C = B
Assertion
Ref Expression
syl6reqr (φC = A)

Proof of Theorem syl6reqr
StepHypRef Expression
1 syl6reqr.1 . 2 (φA = B)
2 syl6reqr.2 . . 3 C = B
32eqcomi 2357 . 2 B = C
41, 3syl6req 2402 1 (φC = A)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   = wceq 1642 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-11 1746  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-ex 1542  df-cleq 2346 This theorem is referenced by:  iftrue  3668  iffalse  3669  difprsn1  3847  funimacnv  5168  dfimafn  5366  fniinfv  5372  fvco2  5382  fniunfv  5466  isoini  5497  dmmptg  5684  nchoicelem14  6302
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