Theorem pm2.21fal 1335

Description: If a wff and its negation are provable, then falsum is provable. (Contributed by Mario Carneiro, 9-Feb-2017.)

Hypotheses

Ref	Expression
pm2.21fal.1	⊢ (φ → ψ)
pm2.21fal.2	⊢ (φ → ¬ ψ)

Assertion

Ref	Expression
pm2.21fal	⊢ (φ → ⊥ )

Proof of Theorem pm2.21fal

Step	Hyp	Ref	Expression
1		pm2.21fal.1	. 2 ⊢ (φ → ψ)
2		pm2.21fal.2	. 2 ⊢ (φ → ¬ ψ)
3	1, 2	pm2.21dd 99	1 ⊢ (φ → ⊥ )

Syntax hints:  ¬ wn 3   → wi 4   ⊥ wfal 1317

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem is referenced by: (None)