Theorem mbifwd-P2.1a 101

Description: Motivation for ↔ Definition, Part A.

Hypothesis

Ref	Expression
mbifwd-P2.1a.1	⊢ ¬ ((𝜑 → 𝜓) → ¬ (𝜓 → 𝜑))

Assertion

Ref	Expression
mbifwd-P2.1a	⊢ (𝜑 → 𝜓)

Proof of Theorem mbifwd-P2.1a

Step	Hyp	Ref	Expression
1		mbifwd-P2.1a.1	. 2 ⊢ ¬ ((𝜑 → 𝜓) → ¬ (𝜓 → 𝜑))
2	1	simpl-L2.2a.SH 96	1 ⊢ (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: (None)