Theorem syl6ssr 2108

Description: A chained subclass and equality deduction.

Hypotheses

Ref	Expression
syl6ssr.1	|- (ph -> A (_ B)
syl6ssr.2	|- C = B

Assertion

Ref	Expression
syl6ssr	|- (ph -> A (_ C)

Proof of Theorem syl6ssr

Step	Hyp	Ref	Expression
1		syl6ssr.1	. 2 |- (ph -> A (_ B)
2		syl6ssr.2	. . 3 |- C = B
3	2	eqcomi 1479	. 2 |- B = C
4	1, 3	syl6ss 2107	1 |- (ph -> A (_ C)

Syntax hints:   -> wi 3   = wceq 956   (_ wss 2047

This theorem is referenced by:  iunpw 2914  tfrlem9 3919  tfrlem13 3923  tz7.49 3959  cplem1 4720  zorn2lem2 4789  infxpidmlem5 7556  eltopss 7603  elcls3 7711  mdsymlem1 10330  idhme 10522

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 962  ax-gen 963  ax-8 964  ax-10 966  ax-12 968  ax-17 971  ax-4 973  ax-5o 975  ax-6o 978  ax-9o 1123  ax-10o 1140  ax-16 1210  ax-11o 1218  ax-ext 1459

This theorem depends on definitions:  df-bi 147  df-an 225  df-ex 981  df-sb 1172  df-clab 1464  df-cleq 1469  df-clel 1472  df-in 2051  df-ss 2053

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