Theorem dalloverim-P7.GENF.RC 1027

Description: Inference form of dalloverim-P7.GENF 1025. †

Hypothesis

Ref	Expression
dalloverim-P7.GENF.RC.1	⊢ (𝜑 → (𝜓 → 𝜒))

Assertion

Ref	Expression
dalloverim-P7.GENF.RC	⊢ (∀𝑥𝜑 → (∀𝑥𝜓 → ∀𝑥𝜒))

Proof of Theorem dalloverim-P7.GENF.RC

Step	Hyp	Ref	Expression
1		ndnfrv-P7.1 826	. . 3 ⊢ Ⅎ𝑥⊤
2		dalloverim-P7.GENF.RC.1	. . . 4 ⊢ (𝜑 → (𝜓 → 𝜒))
3	2	ndtruei-P3.17 182	. . 3 ⊢ (⊤ → (𝜑 → (𝜓 → 𝜒)))
4	1, 3	dalloverim-P7.GENF 1025	. 2 ⊢ (⊤ → (∀𝑥𝜑 → (∀𝑥𝜓 → ∀𝑥𝜒)))
5	4	ndtruee-P3.18 183	1 ⊢ (∀𝑥𝜑 → (∀𝑥𝜓 → ∀𝑥𝜒))

Syntax hints:  ∀wff-forall 8   → wff-imp 10  ⊤wff-true 153

This theorem was proved from axioms:  ax-L1 11  ax-L2 12  ax-L3 13  ax-MP 14  ax-GEN 15  ax-L4 16  ax-L5 17  ax-L6 18  ax-L7 19  ax-L10 27  ax-L11 28  ax-L12 29

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  df-psub-D6.2 716

This theorem is referenced by:  example-E7.1b  1075