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Theorem syl56 34
Description: Combine syl5 32 and syl6 33. (Contributed by NM, 14-Nov-2013.)
Hypotheses
Ref Expression
syl56.1 (𝜑𝜓)
syl56.2 (𝜒 → (𝜓𝜃))
syl56.3 (𝜃𝜏)
Assertion
Ref Expression
syl56 (𝜒 → (𝜑𝜏))

Proof of Theorem syl56
StepHypRef Expression
1 syl56.1 . 2 (𝜑𝜓)
2 syl56.2 . . 3 (𝜒 → (𝜓𝜃))
3 syl56.3 . . 3 (𝜃𝜏)
42, 3syl6 33 . 2 (𝜒 → (𝜓𝜏))
51, 4syl5 32 1 (𝜒 → (𝜑𝜏))
Colors of variables: wff set class
Syntax hints:  wi 4
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7
This theorem is referenced by:  cbv2h  1725  euind  2874  reuind  2892  sbcimdv  2977  cores  5049  prnmaxl  7319  prnminu  7320
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