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Mirrors > Home > MPE Home > Th. List > 19.23bi | Structured version Visualization version GIF version |
Description: Inference form of Theorem 19.23 of [Margaris] p. 90, see 19.23 2211. (Contributed by NM, 12-Mar-1993.) |
Ref | Expression |
---|---|
19.23bi.1 | ⊢ (∃𝑥𝜑 → 𝜓) |
Ref | Expression |
---|---|
19.23bi | ⊢ (𝜑 → 𝜓) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 19.8a 2180 | . 2 ⊢ (𝜑 → ∃𝑥𝜑) | |
2 | 19.23bi.1 | . 2 ⊢ (∃𝑥𝜑 → 𝜓) | |
3 | 1, 2 | syl 17 | 1 ⊢ (𝜑 → 𝜓) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∃wex 1787 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1803 ax-4 1817 ax-5 1918 ax-6 1976 ax-7 2016 ax-12 2177 |
This theorem depends on definitions: df-bi 210 df-ex 1788 |
This theorem is referenced by: nf5ri 2195 equs5eALT 2368 equs5e 2459 2mo 2651 copsexg 5390 axreg2 9236 hash1to3 14087 ustuqtop4 23171 f1omptsnlem 35276 mptsnunlem 35278 |
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