![]() |
Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > ILE Home > Th. List > r19.29a | GIF version |
Description: A commonly used pattern based on r19.29 2624. (Contributed by Thierry Arnoux, 22-Nov-2017.) |
Ref | Expression |
---|---|
r19.29a.1 | ⊢ (((𝜑 ∧ 𝑥 ∈ 𝐴) ∧ 𝜓) → 𝜒) |
r19.29a.2 | ⊢ (𝜑 → ∃𝑥 ∈ 𝐴 𝜓) |
Ref | Expression |
---|---|
r19.29a | ⊢ (𝜑 → 𝜒) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfv 1538 | . 2 ⊢ Ⅎ𝑥𝜑 | |
2 | r19.29a.1 | . 2 ⊢ (((𝜑 ∧ 𝑥 ∈ 𝐴) ∧ 𝜓) → 𝜒) | |
3 | r19.29a.2 | . 2 ⊢ (𝜑 → ∃𝑥 ∈ 𝐴 𝜓) | |
4 | 1, 2, 3 | r19.29af 2628 | 1 ⊢ (𝜑 → 𝜒) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∧ wa 104 ∈ wcel 2158 ∃wrex 2466 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-5 1457 ax-gen 1459 ax-ie1 1503 ax-ie2 1504 ax-4 1520 ax-17 1536 ax-ial 1544 ax-i5r 1545 |
This theorem depends on definitions: df-bi 117 df-tru 1366 df-nf 1471 df-ral 2470 df-rex 2471 |
This theorem is referenced by: cnegexlem3 8147 cnegex 8148 modqmuladdnn0 10381 uzwodc 12051 1arith 12378 mhmid 13007 mhmmnd 13008 ghmgrp 13010 ringinvnz1ne0 13284 neitx 13995 |
Copyright terms: Public domain | W3C validator |