Theorem pfbycase-P1.17.AC.2SH 90

Description: Deductive Form of pfbycase-P1.17 88.

Hypotheses

Ref	Expression
pfbycase-P1.17.AC.2SH.1	⊢ (𝛾 → (𝜑 → 𝜓))
pfbycase-P1.17.AC.2SH.2	⊢ (𝛾 → (¬ 𝜑 → 𝜓))

Assertion

Ref	Expression
pfbycase-P1.17.AC.2SH	⊢ (𝛾 → 𝜓)

Proof of Theorem pfbycase-P1.17.AC.2SH

Step	Hyp	Ref	Expression
1		pfbycase-P1.17.AC.2SH.2	. 2 ⊢ (𝛾 → (¬ 𝜑 → 𝜓))
2		pfbycase-P1.17.AC.2SH.1	. . . 4 ⊢ (𝛾 → (𝜑 → 𝜓))
3		pfbycase-P1.17 88	. . . . . 6 ⊢ ((𝜑 → 𝜓) → ((¬ 𝜑 → 𝜓) → 𝜓))
4	3	axL1.SH 30	. . . . 5 ⊢ (𝛾 → ((𝜑 → 𝜓) → ((¬ 𝜑 → 𝜓) → 𝜓)))
5	4	rcp-FR1.SH 40	. . . 4 ⊢ ((𝛾 → (𝜑 → 𝜓)) → (𝛾 → ((¬ 𝜑 → 𝜓) → 𝜓)))
6	2, 5	ax-MP 14	. . 3 ⊢ (𝛾 → ((¬ 𝜑 → 𝜓) → 𝜓))
7	6	rcp-FR1.SH 40	. 2 ⊢ ((𝛾 → (¬ 𝜑 → 𝜓)) → (𝛾 → 𝜓))
8	1, 7	ax-MP 14	1 ⊢ (𝛾 → 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:  orelim-P2.11c  150