Theorem ndexi-P7.19.RC 886

Description: Inference Form of ndexi-P7.19 844. †

Hypothesis

Ref	Expression
ndexi-P7.19.RC.1	⊢ [𝑡 / 𝑥]𝜑

Assertion

Ref	Expression
ndexi-P7.19.RC	⊢ ∃𝑥𝜑

Proof of Theorem ndexi-P7.19.RC

Step	Hyp	Ref	Expression
1		ndexi-P7.19.RC.1	. . . 4 ⊢ [𝑡 / 𝑥]𝜑
2	1	ndtruei-P3.17 182	. . 3 ⊢ (⊤ → [𝑡 / 𝑥]𝜑)
3	2	ndexi-P7.19 844	. 2 ⊢ (⊤ → ∃𝑥𝜑)
4	3	ndtruee-P3.18 183	1 ⊢ ∃𝑥𝜑

Syntax hints:  ⊤wff-true 153  ∃wff-exists 595  [wff-psub 714

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

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-psub-D6.2 716

This theorem is referenced by:  axL6ex-P7  925