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Theorem pm13.181OLD 3018
Description: Obsolete version of pm13.181 3017 as of 30-Oct-2024. (Contributed by Andrew Salmon, 3-Jun-2011.) (New usage is discouraged.) (Proof modification is discouraged.)
Assertion
Ref Expression
pm13.181OLD ((𝐴 = 𝐵𝐵𝐶) → 𝐴𝐶)

Proof of Theorem pm13.181OLD
StepHypRef Expression
1 eqcom 2733 . 2 (𝐴 = 𝐵𝐵 = 𝐴)
2 pm13.18 3016 . 2 ((𝐵 = 𝐴𝐵𝐶) → 𝐴𝐶)
31, 2sylanb 580 1 ((𝐴 = 𝐵𝐵𝐶) → 𝐴𝐶)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 395   = wceq 1533  wne 2934
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1905  ax-6 1963  ax-7 2003  ax-9 2108  ax-ext 2697
This theorem depends on definitions:  df-bi 206  df-an 396  df-ex 1774  df-cleq 2718  df-ne 2935
This theorem is referenced by: (None)
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