True Statement is implied by Every Statement

Theorem

If something is true, then anything implies it.

Formulation 1

\(\ds p\) \(\) \(\ds \)
\(\ds \vdash \ \ \) \(\ds q \implies p\) \(\) \(\ds \)

Formulation 2

$\vdash q \implies \paren {p \implies q}$


Also see


Sources

  • 1959: A.H. Basson and D.J. O'Connor: Introduction to Symbolic Logic (3rd ed.) ... (previous) ... (next): $\S 2.3$: Basic Truth-Tables of the Propositional Calculus
  • 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): implication: 1. (material implication)
  • 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): implication: 1. (material implication)
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