Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > MPE Home > Th. List > rexpr | Structured version Visualization version Unicode version |
Description: Convert an existential quantification over a pair to a disjunction. (Contributed by NM, 3-Jun-2007.) (Revised by Mario Carneiro, 23-Apr-2015.) |
Ref | Expression |
---|---|
ralpr.1 | |
ralpr.2 | |
ralpr.3 | |
ralpr.4 |
Ref | Expression |
---|---|
rexpr |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ralpr.1 | . 2 | |
2 | ralpr.2 | . 2 | |
3 | ralpr.3 | . . 3 | |
4 | ralpr.4 | . . 3 | |
5 | 3, 4 | rexprg 4235 | . 2 |
6 | 1, 2, 5 | mp2an 708 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 196 wo 383 wceq 1483 wcel 1990 wrex 2913 cvv 3200 cpr 4179 |
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-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-3an 1039 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-rex 2918 df-v 3202 df-sbc 3436 df-un 3579 df-sn 4178 df-pr 4180 |
This theorem is referenced by: xpsdsval 22186 poimir 33442 |
Copyright terms: Public domain | W3C validator |