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Theorem sylan9ssr 3184
Description: A subclass transitivity deduction. (Contributed by NM, 27-Sep-2004.)
Hypotheses
Ref Expression
sylan9ssr.1 (𝜑𝐴𝐵)
sylan9ssr.2 (𝜓𝐵𝐶)
Assertion
Ref Expression
sylan9ssr ((𝜓𝜑) → 𝐴𝐶)

Proof of Theorem sylan9ssr
StepHypRef Expression
1 sylan9ssr.1 . . 3 (𝜑𝐴𝐵)
2 sylan9ssr.2 . . 3 (𝜓𝐵𝐶)
31, 2sylan9ss 3183 . 2 ((𝜑𝜓) → 𝐴𝐶)
43ancoms 268 1 ((𝜓𝜑) → 𝐴𝐶)
Colors of variables: wff set class
Syntax hints:  wi 4  wa 104  wss 3144
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1458  ax-7 1459  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-8 1515  ax-11 1517  ax-4 1521  ax-17 1537  ax-i9 1541  ax-ial 1545  ax-i5r 1546  ax-ext 2171
This theorem depends on definitions:  df-bi 117  df-nf 1472  df-sb 1774  df-clab 2176  df-cleq 2182  df-clel 2185  df-in 3150  df-ss 3157
This theorem is referenced by:  intssuni2m  3883
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