Theorem tbw-ax1 1733

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 84	1 ⊢ ((𝜑 → 𝜓) → ((𝜓 → 𝜒) → (𝜑 → 𝜒)))

This proof depends on syntax axioms:   → wi 4

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7

This theorem is used by:  tbwsyl  1737  tbwlem1  1738  tbwlem2  1739  tbwlem3  1740  tbwlem4  1741  tbwlem5  1742  re1luk1  1743  re1luk2  1744  re1luk3  1745