Theorem simpl-P2.9a.AC.SH 135

Description: Deductive Form of simpl-P2.9a 134.

Hypothesis

Ref	Expression
simpl-P2.9a.AC.SH.1	⊢ (𝛾 → (𝜑 ∧ 𝜓))

Assertion

Ref	Expression
simpl-P2.9a.AC.SH	⊢ (𝛾 → 𝜑)

Proof of Theorem simpl-P2.9a.AC.SH

Step	Hyp	Ref	Expression
1		simpl-P2.9a.AC.SH.1	. 2 ⊢ (𝛾 → (𝜑 ∧ 𝜓))
2		simpl-P2.9a 134	. . . 4 ⊢ ((𝜑 ∧ 𝜓) → 𝜑)
3	2	axL1.SH 30	. . 3 ⊢ (𝛾 → ((𝜑 ∧ 𝜓) → 𝜑))
4	3	rcp-FR1.SH 40	. 2 ⊢ ((𝛾 → (𝜑 ∧ 𝜓)) → (𝛾 → 𝜑))
5	1, 4	ax-MP 14	1 ⊢ (𝛾 → 𝜑)

Syntax hints:   → 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:  orelim-P2.11c  150  ndander-P3.9  174