Theorem tbw-ax1 1465

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 70	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  1469  tbwlem1  1470  tbwlem2  1471  tbwlem3  1472  tbwlem4  1473  tbwlem5  1474  re1luk1  1475  re1luk2  1476  re1luk3  1477