Theorem poe-P1.11b 66

Description: Principle of Explosion B.

A contradiction implies anything. The other form is poe-P1.11a 65.

Assertion

Ref	Expression
poe-P1.11b	⊢ (𝜑 → (¬ 𝜑 → 𝜓))

Proof of Theorem poe-P1.11b

Step	Hyp	Ref	Expression
1		poe-P1.11a 65	. 2 ⊢ (¬ 𝜑 → (𝜑 → 𝜓))
2	1	imcomm-P1.6.SH 49	1 ⊢ (𝜑 → (¬ 𝜑 → 𝜓))

Syntax hints:  ¬ wff-neg 9   → wff-imp 10

This theorem was proved from axioms:  ax-L1 11  ax-L2 12  ax-L3 13  ax-MP 14

This theorem is referenced by:  poe-P1.11b.AC.2SH  67  orintl-P2.11a  146  orintr-P2.11b  148