Theorem ndnfrbi-P7.6.CL 908

Description: Closed Form of ndnfrbi-P7.6 831. †

Assertion

Ref	Expression
ndnfrbi-P7.6.CL	⊢ ((Ⅎ𝑥𝜑 ∧ Ⅎ𝑥𝜓) → Ⅎ𝑥(𝜑 ↔ 𝜓))

Proof of Theorem ndnfrbi-P7.6.CL

Step	Hyp	Ref	Expression
1		rcp-NDASM1of2 193	. 2 ⊢ ((Ⅎ𝑥𝜑 ∧ Ⅎ𝑥𝜓) → Ⅎ𝑥𝜑)
2		rcp-NDASM2of2 194	. 2 ⊢ ((Ⅎ𝑥𝜑 ∧ Ⅎ𝑥𝜓) → Ⅎ𝑥𝜓)
3	1, 2	ndnfrbi-P7.6 831	1 ⊢ ((Ⅎ𝑥𝜑 ∧ Ⅎ𝑥𝜓) → Ⅎ𝑥(𝜑 ↔ 𝜓))

Syntax hints:   → wff-imp 10   ↔ wff-bi 104   ∧ wff-and 132  Ⅎwff-nfree 681

This theorem was proved from axioms:  ax-L1 11  ax-L2 12  ax-L3 13  ax-MP 14  ax-GEN 15  ax-L4 16

This theorem depends on definitions:  df-bi-D2.1 107  df-and-D2.2 133  df-or-D2.3 145  df-true-D2.4 155  df-rcp-AND3 161  df-exists-D5.1 596  df-nfree-D6.1 682

This theorem is referenced by: (None)