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Mirrors > Home > ILE Home > Th. List > op1std | Unicode version |
Description: Extract the first member of an ordered pair. (Contributed by Mario Carneiro, 31-Aug-2015.) |
Ref | Expression |
---|---|
op1st.1 |
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op1st.2 |
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Ref | Expression |
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op1std |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | fveq2 5429 |
. 2
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2 | op1st.1 |
. . 3
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3 | op1st.2 |
. . 3
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4 | 2, 3 | op1st 6052 |
. 2
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5 | 1, 4 | eqtrdi 2189 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 699 ax-5 1424 ax-7 1425 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1483 ax-10 1484 ax-11 1485 ax-i12 1486 ax-bndl 1487 ax-4 1488 ax-13 1492 ax-14 1493 ax-17 1507 ax-i9 1511 ax-ial 1515 ax-i5r 1516 ax-ext 2122 ax-sep 4054 ax-pow 4106 ax-pr 4139 ax-un 4363 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1335 df-nf 1438 df-sb 1737 df-eu 2003 df-mo 2004 df-clab 2127 df-cleq 2133 df-clel 2136 df-nfc 2271 df-ral 2422 df-rex 2423 df-v 2691 df-sbc 2914 df-un 3080 df-in 3082 df-ss 3089 df-pw 3517 df-sn 3538 df-pr 3539 df-op 3541 df-uni 3745 df-br 3938 df-opab 3998 df-mpt 3999 df-id 4223 df-xp 4553 df-rel 4554 df-cnv 4555 df-co 4556 df-dm 4557 df-rn 4558 df-iota 5096 df-fun 5133 df-fv 5139 df-1st 6046 |
This theorem is referenced by: xp1st 6071 sbcopeq1a 6093 csbopeq1a 6094 eloprabi 6102 mpomptsx 6103 dmmpossx 6105 fmpox 6106 fmpoco 6121 df1st2 6124 xporderlem 6136 xpf1o 6746 fisumcom2 11239 txbas 12466 cnmpt1st 12496 txhmeo 12527 |
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