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Theorem sylan9ssr 2936
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 2935 . 2 ((φ ψ) → A𝐶)
43ancoms 255 1 ((ψ φ) → A𝐶)
Colors of variables: wff set class
Syntax hints:  wi 4   wa 97  wss 2894
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 1316  ax-7 1317  ax-gen 1318  ax-ie1 1363  ax-ie2 1364  ax-8 1376  ax-11 1378  ax-4 1381  ax-17 1400  ax-i9 1404  ax-ial 1409  ax-i5r 1410  ax-ext 2004
This theorem depends on definitions:  df-bi 110  df-nf 1330  df-sb 1628  df-clab 2009  df-cleq 2015  df-clel 2018  df-in 2901  df-ss 2908
This theorem is referenced by:  intssuni2m  3613
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