Theorem exe-P7r.RC.VR 1003

Description: exe-P7r.RC 1002 with variable restriction. †

'𝑥' cannot occur in '𝜓'.

Hypotheses

Ref	Expression
exe-P7r.RC.VR.1	⊢ (𝜑 → 𝜓)
exe-P7r.RC.VR.2	⊢ ∃𝑥𝜑

Assertion

Ref	Expression
exe-P7r.RC.VR	⊢ 𝜓

Distinct variable group:   𝜓,𝑥

Proof of Theorem exe-P7r.RC.VR

Step	Hyp	Ref	Expression
1		ndnfrv-P7.1 826	. 2 ⊢ Ⅎ𝑥𝜓
2		exe-P7r.RC.VR.1	. 2 ⊢ (𝜑 → 𝜓)
3		exe-P7r.RC.VR.2	. 2 ⊢ ∃𝑥𝜑
4	1, 2, 3	exe-P7r.RC 1002	1 ⊢ 𝜓

Syntax hints:   → wff-imp 10  ∃wff-exists 595

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:  nfrsucc-P8  1119  nfradd-P8  1120  nfrmult-P8  1121