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Theorem sylan9ssr 2953
Description: A subclass transitivity deduction. (Contributed by NM, 27-Sep-2004.)
Hypotheses
Ref Expression
sylan9ssr.1 (φAB)
sylan9ssr.2 (ψB𝐶)
Assertion
Ref Expression
sylan9ssr ((ψ φ) → A𝐶)

Proof of Theorem sylan9ssr
StepHypRef Expression
1 sylan9ssr.1 . . 3 (φAB)
2 sylan9ssr.2 . . 3 (ψB𝐶)
31, 2sylan9ss 2952 . 2 ((φ ψ) → A𝐶)
43ancoms 255 1 ((ψ φ) → A𝐶)
Colors of variables: wff set class
Syntax hints:  wi 4   wa 97  wss 2911
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-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-11 1394  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-in 2918  df-ss 2925
This theorem is referenced by:  intssuni2m  3630
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