Theorem simpl-P2.9a 134

Description: '∧' Left Simplification.

Assertion

Ref	Expression
simpl-P2.9a	⊢ ((𝜑 ∧ 𝜓) → 𝜑)

Proof of Theorem simpl-P2.9a

Step	Hyp	Ref	Expression
1		df-and-D2.2 133	. . 3 ⊢ ((𝜑 ∧ 𝜓) ↔ ¬ (𝜑 → ¬ 𝜓))
2	1	bifwd-P2.5a.SH 112	. 2 ⊢ ((𝜑 ∧ 𝜓) → ¬ (𝜑 → ¬ 𝜓))
3		simpl-L2.2a 95	. 2 ⊢ (¬ (𝜑 → ¬ 𝜓) → 𝜑)
4	2, 3	syl-P1.2 34	1 ⊢ ((𝜑 ∧ 𝜓) → 𝜑)

Syntax hints:  ¬ wff-neg 9   → wff-imp 10   ∧ wff-and 132

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

This theorem depends on definitions:  df-bi-D2.1 107  df-and-D2.2 133

This theorem is referenced by:  simpl-P2.9a.AC.SH  135  import-P2.10a  140  orelim-P2.11c  150