Theorem tbw-ax1 1697

Description: The first of four axioms in the Tarski-Bernays-Wajsberg system. (Contributed by Anthony Hart, 13-Aug-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

Ref	Expression
tbw-ax1	⊢ ((𝜑 → 𝜓) → ((𝜓 → 𝜒) → (𝜑 → 𝜒)))

Proof of Theorem tbw-ax1

Step	Hyp	Ref	Expression
1		imim1 83	1 ⊢ ((𝜑 → 𝜓) → ((𝜓 → 𝜒) → (𝜑 → 𝜒)))

Syntax hints:   → wi 4

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7

This theorem is referenced by:  tbwsyl  1701  tbwlem1  1702  tbwlem2  1703  tbwlem3  1704  tbwlem4  1705  tbwlem5  1706  re1luk1  1707  re1luk2  1708  re1luk3  1709