Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > MPE Home > Th. List > exanOLDOLD | Structured version Visualization version GIF version |
Description: Obsolete proof of exan 1788 as of 7-Jul-2021. (Contributed by NM, 18-Aug-1993.) (Proof shortened by Andrew Salmon, 25-May-2011.) (Proof shortened by Wolf Lammen, 13-Jan-2018.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
exanOLDOLD.1 | ⊢ (∃𝑥𝜑 ∧ 𝜓) |
Ref | Expression |
---|---|
exanOLDOLD | ⊢ ∃𝑥(𝜑 ∧ 𝜓) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | exanOLDOLD.1 | . 2 ⊢ (∃𝑥𝜑 ∧ 𝜓) | |
2 | 1 | simpri 478 | . . . 4 ⊢ 𝜓 |
3 | 2 | nfth 1727 | . . 3 ⊢ Ⅎ𝑥𝜓 |
4 | 3 | 19.41 2103 | . 2 ⊢ (∃𝑥(𝜑 ∧ 𝜓) ↔ (∃𝑥𝜑 ∧ 𝜓)) |
5 | 1, 4 | mpbir 221 | 1 ⊢ ∃𝑥(𝜑 ∧ 𝜓) |
Colors of variables: wff setvar class |
Syntax hints: ∧ wa 384 ∃wex 1704 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-12 2047 |
This theorem depends on definitions: df-bi 197 df-an 386 df-ex 1705 df-nf 1710 |
This theorem is referenced by: (None) |
Copyright terms: Public domain | W3C validator |