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Theorem tbsyl 32506
Description: The weak syllogism from Tarski-Bernays'. (Contributed by Anthony Hart, 16-Aug-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
tbsyl.1 (𝜑𝜓)
tbsyl.2 (𝜓𝜒)
Assertion
Ref Expression
tbsyl (𝜑𝜒)

Proof of Theorem tbsyl
StepHypRef Expression
1 tbsyl.2 . 2 (𝜓𝜒)
2 tbsyl.1 . . 3 (𝜑𝜓)
3 tb-ax1 32503 . . 3 ((𝜑𝜓) → ((𝜓𝜒) → (𝜑𝜒)))
42, 3ax-mp 5 . 2 ((𝜓𝜒) → (𝜑𝜒))
51, 4ax-mp 5 1 (𝜑𝜒)
Colors of variables: wff setvar 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:  re1ax2lem  32507  re1ax2  32508
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