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Mirrors > Home > MPE Home > Th. List > Mathboxes > e22 | Structured version Visualization version GIF version |
Description: A virtual deduction elimination rule. (Contributed by Alan Sare, 2-May-2011.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
e22.1 | ⊢ ( 𝜑 , 𝜓 ▶ 𝜒 ) |
e22.2 | ⊢ ( 𝜑 , 𝜓 ▶ 𝜃 ) |
e22.3 | ⊢ (𝜒 → (𝜃 → 𝜏)) |
Ref | Expression |
---|---|
e22 | ⊢ ( 𝜑 , 𝜓 ▶ 𝜏 ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | e22.1 | . 2 ⊢ ( 𝜑 , 𝜓 ▶ 𝜒 ) | |
2 | e22.2 | . 2 ⊢ ( 𝜑 , 𝜓 ▶ 𝜃 ) | |
3 | e22.3 | . . 3 ⊢ (𝜒 → (𝜃 → 𝜏)) | |
4 | 3 | a1i 11 | . 2 ⊢ (𝜒 → (𝜒 → (𝜃 → 𝜏))) |
5 | 1, 1, 2, 4 | e222 38861 | 1 ⊢ ( 𝜑 , 𝜓 ▶ 𝜏 ) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ( wvd2 38793 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 |
This theorem depends on definitions: df-bi 197 df-an 386 df-vd2 38794 |
This theorem is referenced by: e22an 38897 e02 38922 e12 38951 e20 38954 e21 38957 sspwtr 39048 pwtrVD 39059 pwtrrVD 39060 elex22VD 39074 tpid3gVD 39077 en3lplem2VD 39079 imbi12VD 39109 truniALTVD 39114 trintALTVD 39116 onfrALTlem3VD 39123 onfrALTlem2VD 39125 ax6e2eqVD 39143 ax6e2ndeqVD 39145 sb5ALTVD 39149 |
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