Theorem tbw-ax1 1616

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 81	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  1620  tbwlem1  1621  tbwlem2  1622  tbwlem3  1623  tbwlem4  1624  tbwlem5  1625  re1luk1  1626  re1luk2  1627  re1luk3  1628