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Mirrors > Home > MPE Home > Th. List > 19.21bi | Structured version Visualization version GIF version |
Description: Inference form of 19.21 2062 and also deduction form of sp 2041. (Contributed by NM, 26-May-1993.) |
Ref | Expression |
---|---|
19.21bi.1 | ⊢ (𝜑 → ∀𝑥𝜓) |
Ref | Expression |
---|---|
19.21bi | ⊢ (𝜑 → 𝜓) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 19.21bi.1 | . 2 ⊢ (𝜑 → ∀𝑥𝜓) | |
2 | sp 2041 | . 2 ⊢ (∀𝑥𝜓 → 𝜓) | |
3 | 1, 2 | syl 17 | 1 ⊢ (𝜑 → 𝜓) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∀wal 1473 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1713 ax-4 1728 ax-5 1827 ax-6 1875 ax-7 1922 ax-12 2034 |
This theorem depends on definitions: df-bi 196 df-ex 1696 |
This theorem is referenced by: 19.21bbi 2048 eqeq1dALT 2613 eleq2dALT 2675 ssel 3562 pocl 4966 funmo 5820 funun 5846 fununi 5878 findcard 8084 findcard2 8085 axpowndlem4 9301 axregndlem2 9304 axinfnd 9307 prcdnq 9694 dfrtrcl2 13650 relexpindlem 13651 bnj1379 30155 bnj1052 30297 bnj1118 30306 bnj1154 30321 bnj1280 30342 dftrcl3 37031 dfrtrcl3 37044 vk15.4j 37755 hbimpg 37791 |
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